{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/16.jpg' \/><\/center> Ph\u00e2n t\u00edch \u0111a th\u1ee9c $x^4+2x^3+2x^2+2x+1$ th\u00e0nh nh\u00e2n t\u1eed th\u00ec s\u1ebd c\u00f3 m\u1ed9t nh\u00e2n t\u1eed l\u00e0: ","select":["A. $1-x$ ","B. $(x+1)^2$ ","C. $(x-1)^2$","D. $x^2-1$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> Nh\u00f3m $\\left( {{x}^{4}}+2{{x}^{2}}+1 \\right)+\\left( 2{{x}^{3}}+2x \\right)$. <br\/><b> B\u01b0\u1edbc 2: <\/b>Ti\u1ebfp t\u1ee5c ph\u00e2n t\u00edch b\u1eb1ng c\u00e1ch \u0111\u1eb7t nh\u00e2n t\u1eed chung v\u00e0 d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3 :<br\/> $\\begin{align} & {{x}^{4}}+2{{x}^{3}}+2{{x}^{2}}+2x+1 \\\\ & =\\left( {{x}^{4}}+2{{x}^{2}}+1 \\right)+\\left( 2{{x}^{3}}+2x \\right) \\\\ & ={{\\left( {{x}^{2}}+1 \\right)}^{2}}+2x\\left( {{x}^{2}}+1 \\right) \\\\ & =\\left( {{x}^{2}}+1 \\right)\\left( {{x}^{2}}+1+2x \\right) \\\\ & =\\left( {{x}^{2}}+1 \\right){{\\left( x+1 \\right)}^{2}} \\\\ \\end{align}$ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":621},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/13.jpg' \/><\/center> Ph\u00e2n t\u00edch \u0111a th\u1ee9c $(x+y)^2+3(x+y)+2$ th\u00e0nh nh\u00e2n t\u1eed th\u00ec s\u1ebd c\u00f3 m\u1ed9t nh\u00e2n t\u1eed l\u00e0: ","select":["A. $x+y$ ","B. $x+y-2$ ","C. $x-y-1$","D. $x+y+1$"],"hint":" \u0110\u1eb7t $x+y=t$. Ph\u00e2n t\u00edch \u0111a th\u1ee9c theo bi\u1ebfn t. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> \u0110\u1eb7t $x+y=t$, \u0111\u01b0\u1ee3c $t^2+3t+2=t^2+t+2t+2$. <br\/><b> B\u01b0\u1edbc 2: <\/b>T\u00e1ch $3t = 2t + t$, ph\u00e2n t\u00edch \u0111a th\u1ee9c b\u1eb1ng c\u00e1ch \u0111\u1eb7t nh\u00e2n t\u1eed chung.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta \u0111\u1eb7t $x+y=t$ <br\/> $\\begin{align} & {{(x+y)}^{2}}+3(x+y)+2 \\\\ & ={{t}^{2}}+3t+2 \\\\ & ={{t}^{2}}+t+2t+2 \\\\ & =t\\left( t+1 \\right)+2\\left( t+1 \\right) \\\\ & =\\left( t+1 \\right)\\left( t+2 \\right) \\\\ & =\\left( x+y+1 \\right)\\left( x+y+2 \\right) \\\\ \\end{align}$ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 D.<\/span>","column":2}]}],"id_ques":622},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/10.jpg' \/><\/center> \u0110a th\u1ee9c $A=x^4+x^2+2x$ c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng 0 th\u00ec:","select":["A. $x=0$ ho\u1eb7c $x=1$ ","B. $x=0$ ho\u1eb7c $x=-1$ ","C. $x=0$ ho\u1eb7c $x=2$","D. $x=0$ ho\u1eb7c $x=-2$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b> B\u01b0\u1edbc 1: <\/b> T\u00e1ch: ${{x}^{4}}+{{x}^{2}}+2x$$={{x}^{4}}-1+{{x}^{2}}+2x+1$.<br\/> <b> B\u01b0\u1edbc 2: <\/b> Ph\u00e2n t\u00edch ti\u1ebfp theo c\u00e1ch \u0111\u1eb7t nh\u00e2n t\u1eed chung v\u00e0 s\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c.<br\/><b> B\u01b0\u1edbc 3:<\/b> T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 $A = 0$.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/><span class='basic_left'>$\\begin{align} & A={{x}^{4}}+{{x}^{2}}+2x \\\\ & ={{x}^{4}}-1+{{x}^{2}}+2x+1 \\\\ & =\\left( {{x}^{2}}+1 \\right)\\left( {{x}^{2}}-1 \\right)+{{\\left( x+1 \\right)}^{2}} \\\\ & =\\left( {{x}^{2}}+1 \\right)\\left( x+1 \\right)\\left( x-1 \\right)+{{\\left( x+1 \\right)}^{2}} \\\\ & =\\left( x+1 \\right)\\left[ \\left( {{x}^{2}}+1 \\right)\\left( x-1 \\right)+\\left( x+1 \\right) \\right] \\\\ & =\\left( x+1 \\right)\\left( {{x}^{3}}-{{x}^{2}}+x-1+x+1 \\right) \\\\ & =\\left( x+1 \\right)\\left( {{x}^{3}}-{{x}^{2}}+2x \\right) \\\\ & =\\left( x+1 \\right)x\\left( {{x}^{2}}-x+2 \\right) \\\\ \\end{align}$ <br\/>\u0110\u1ec3 $A = 0$ th\u00ec: <br\/>$\\begin{aligned} & \\left( x+1 \\right)x\\left( {{x}^{2}}-x+2 \\right)=0 \\\\ & \\Rightarrow \\left[ \\begin{aligned} & x+1=0 \\\\ & x=0 \\\\ & {{x}^{2}}-x+2>0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left[ \\begin{aligned} & x=-1 \\\\ & x=0 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ . <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B<\/span>","column":2}]}],"id_ques":623},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/10.jpg' \/><\/center> \u0110a th\u1ee9c $A=x^3+4x^2+5x+2$ c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng 0 th\u00ec:","select":["A. $x=-1$ ho\u1eb7c $x=-2$ ","B. $x=1$ ho\u1eb7c $x=2$ ","C. $x=2$ ho\u1eb7c $x=3$","D. $x=-2$ ho\u1eb7c $x=-3$"],"hint":" Ph\u00e2n t\u00edch \u0111a th\u1ee9c A th\u00e0nh nh\u00e2n t\u1eed theo c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ed3ng nh\u1ea5t h\u1ec7 s\u1ed1<br\/> \u0110\u1eb7t: ${{x}^{3}}+4{{x}^{2}}+5x+2$ $=\\left( x+a \\right)\\left( {{x}^{2}}+bx+c \\right)$.<br\/> \u0110\u1ed3ng nh\u1ea5t h\u1ec7 s\u1ed1 t\u00ecm a, b, c. <br\/> T\u00ecm \u0111i\u1ec1u ki\u1ec7n \u0111\u1ec3 A = 0. N\u1ebfu a.b = 0 th\u00ec ho\u1eb7c a = 0 ho\u1eb7c b = 0.","explain":"<span class='basic_left'>Ta ph\u00e2n t\u00edch \u0111a th\u1ee9c A th\u00e0nh nh\u00e2n t\u1eed b\u1eb1ng c\u00e1ch \u0111\u1ed3ng nh\u1ea5t h\u1ec7 s\u1ed1.<br\/>$\\begin{align} & A=\\left( x+a \\right)\\left( {{x}^{2}}+bx+c \\right) \\\\ & {{x}^{3}}+4{{x}^{2}}+5x+2=\\left( x+a \\right)\\left( {{x}^{2}}+bx+c \\right) \\\\ & {{x}^{3}}+4{{x}^{2}}+5x+2={{x}^{3}}+\\left( a+b \\right){{x}^{2}}+\\left( ab+c\\right)x+ac \\\\ \\end{align}$ <br\/>\u0110\u1ed3ng nh\u1ea5t h\u1ec7 s\u1ed1 v\u1ebf tr\u00e1i v\u00e0 v\u1ebf ph\u1ea3i:<br\/>$\\left\\{ \\begin{aligned} & a+b=4 \\\\ & ab+c=5 \\\\ & ac=2 \\\\ \\end{aligned} \\right.\\Rightarrow \\left\\{ \\begin{aligned} & a=1 \\\\ & b=3 \\\\ & c=2 \\\\ \\end{aligned} \\right.$ <br\/>Do \u0111\u00f3:<br\/>$\\begin{align} & {{x}^{3}}+4{{x}^{2}}+5x+2 \\\\ & =\\left( x+1 \\right)\\left( {{x}^{2}}+3x+2 \\right) \\\\ & =\\left( x+1 \\right)\\left( {{x}^{2}}+x+2x+2 \\right) \\\\ & =\\left( x+1 \\right)\\left( x+1 \\right)\\left( x+2 \\right) \\\\ & ={{\\left( x+1 \\right)}^{2}}\\left( x+2 \\right) \\\\ \\end{align}$ <br\/> V\u1eady $A = 0$ t\u1ee9c l\u00e0: <br\/>$\\begin{aligned} & {{\\left( x+1 \\right)}^{2}}\\left( x+2 \\right)=0 \\\\ & \\Rightarrow \\left[ \\begin{aligned} & x+1=0 \\\\ & x+2=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left[ \\begin{aligned} & x=-1 \\\\ & x=-2 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$ . <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}]}],"id_ques":624},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/9.jpg' \/><\/center>V\u1edbi $x\\,\\,\\in\\mathbb{R}$ th\u00ec $A=(x^2+1)^4+9(x^2+1)^3+21(x^2+1)^2$$-x^2-31\\le 0$. ","select":["\u0110\u00fang","Sai"],"hint":" \u0110\u1eb7t $x^2+1=t$ \u0111\u01b0\u1ee3c: $A={{t}^{4}}+9{{t}^{3}}+21{{t}^{2}}-t-30$ <br\/> Ph\u00e2n t\u00edch \u0111a th\u1ee9c theo c\u00e1ch t\u00e1ch r\u1ed3i nh\u00f3m: $A={{t}^{4}}-t+9{{t}^{3}}-9{{t}^{2}}+30{{t}^{2}}-30$.<br\/> Thay $t=x^2+1$ l\u1ea1i v\u00e0o \u0111a th\u1ee9c \u0111\u00e3 ph\u00e2n t\u00edch. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b> B\u01b0\u1edbc 1:<\/b> \u0110\u1eb7t $x^2+1=t$ \u0111\u01b0\u1ee3c: $A={{t}^{4}}+9{{t}^{3}}+21{{t}^{2}}-t-30$.<br\/><b> B\u01b0\u1edbc 2:<\/b> Ph\u00e2n t\u00edch \u0111a th\u1ee9c theo c\u00e1ch t\u00e1ch r\u1ed3i nh\u00f3m: $A={{t}^{4}}-t+9{{t}^{3}}-9{{t}^{2}}+30{{t}^{2}}-30$<br\/><b> B\u01b0\u1edbc 3:<\/b> Thay $t=x^2+1$ l\u1ea1i v\u00e0o \u0111a th\u1ee9c \u0111\u00e3 ph\u00e2n t\u00edch.<br\/> <b> B\u01b0\u1edbc 4:<\/b> \u0110\u00e1nh gi\u00e1 xem $A\\le 0$ \u0111\u00fang hay sai. <br\/> <span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'> \u0110\u1eb7t $x^2+1=t$, ta \u0111\u01b0\u1ee3c:<br\/> $ A={{t}^{4}}+9{{t}^{3}}+21{{t}^{2}}-t-30 $ <br\/> $ ={{t}^{4}}-t+9{{t}^{3}}-9{{t}^{2}}+30{{t}^{2}}-30 $ <br\/> $ =t\\left( {{t}^{3}}-1 \\right)+9{{t}^{2}}\\left( t-1 \\right)$$+30\\left( {{t}^{2}}-1 \\right) $<br\/>$ =t\\left( t-1 \\right)\\left( {{t}^{2}}+t+1 \\right)+9{{t}^{2}}\\left( t-1 \\right)$$+30\\left( t+1 \\right)\\left( t-1 \\right) $<br\/>$ =\\left( t-1 \\right)\\left[ t\\left( {{t}^{2}}+t+1 \\right)+9{{t}^{2}}+30\\left( t+1 \\right) \\right] $<br\/>$ =\\left( t-1 \\right)\\left( {{t}^{3}}+{{t}^{2}}+t+9{{t}^{2}}+30t+30 \\right) $<br\/>$ =\\left( t-1 \\right)\\left( {{t}^{3}}+10{{t}^{2}}+31t+30 \\right) $<br\/>$ =\\left( x^2 + 1 - 1 \\right)\\left[(x^2 + 1)^3 + (x^2 + 1)^2 + 9(x^2 + 1) + 30 \\right] $<br\/>$ =x^2 \\left[(x^2 + 1)^3 + (x^2 + 1)^2 + 9(x^2 + 1) + 30 \\right] $<br\/>V\u00ec $x^2 \\ge 0$, $x^2 + 1 \\ge 1$ v\u1edbi m\u1ecdi x<br\/> $\\Rightarrow$ $ x^2 \\left[(x^2 + 1)^3 + (x^2 + 1)^2 + 9(x^2 + 1) + 30 \\right] $ $> 0$ v\u1edbi m\u1ecdi $x$<br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0: Sai.<\/span>","column":2}]}],"id_ques":625},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t.<br\/> Kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/9.jpg' \/><\/center>V\u1edbi $x\\,\\,\\in\\mathbb{Z}$ th\u00ec $B={{x}^{4}}-4{{x}^{3}}-2{{x}^{2}}+12x+9$ l\u00e0 b\u00ecnh ph\u01b0\u01a1ng m\u1ed9t s\u1ed1 nguy\u00ean. ","select":["\u0110\u00fang","Sai"],"hint":" Ph\u00e2n t\u00edch \u0111a th\u1ee9c theo c\u00e1ch t\u00e1ch: $B={{x}^{4}}-4{{x}^{3}}-2{{x}^{2}}+12x+9$$=\\left( {{x}^{4}}-4{{x}^{3}}+4{{x}^{2}} \\right)$$-\\left( 6{{x}^{2}}-12x \\right)+9$.<br\/> Ti\u1ebfp t\u1ee5c ph\u00e2n t\u00edch b\u1eb1ng c\u00e1ch \u0111\u1eb7t nh\u00e2n t\u1eed chung v\u00e0 d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b> B\u01b0\u1edbc 1:<\/b> $B={{x}^{4}}-4{{x}^{3}}-2{{x}^{2}}+12x+9$$=\\left( {{x}^{4}}-4{{x}^{3}}+4{{x}^{2}} \\right)$$-\\left( 6{{x}^{2}}-12x \\right)+9$.<br\/><b> B\u01b0\u1edbc 2:<\/b> Ti\u1ebfp t\u1ee5c ph\u00e2n t\u00edch b\u1eb1ng c\u00e1ch \u0111\u1eb7t nh\u00e2n t\u1eed chung v\u00e0 d\u00f9ng H\u0110T. <br\/> <span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'> Ta c\u00f3:<br\/> $ B={{x}^{4}}-4{{x}^{3}}-2{{x}^{2}}+12x+9 $<br\/>$ =\\left( {{x}^{4}}-4{{x}^{3}}+4{{x}^{2}} \\right)$$-\\left( 6{{x}^{2}}-12x \\right)+9 $<br\/>$ ={{\\left( {{x}^{2}}-2x \\right)}^{2}}-6\\left( {{x}^{2}}-2x \\right)+9 $<br\/>$ ={{\\left( {{x}^{2}}-2x-3 \\right)}^{2}} $<br\/>$ ={{ \\left( {{x}^{2}}+x-3x-3 \\right) \\right)}^{2}} $<br\/>$ ={{\\left[ \\left( x-3 \\right)\\left( x+1 \\right) \\right]}^{2}} $<br\/> Do \u0111\u00f3 $x\\,\\,\\in\\mathbb{Z}$ n\u00ean $B$ l\u00e0 b\u00ecnh ph\u01b0\u01a1ng m\u1ed9t s\u1ed1 nguy\u00ean. <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 \u0110\u00fang.<\/span>","column":2}]}],"id_ques":626},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 v\u00e0o \u00f4 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank_random","correct":[[["-1"],["-6"]]],"list":[{"point":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/5.jpg' \/><\/center> Bi\u1ebft $(x+2)(x+3)(x+4)(x+5)$$-24=0$, gi\u00e1 tr\u1ecb $\\left[ \\begin{align} & x= \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\\\ & x=\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ \\end{align} \\right.$ ","hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b>B\u01b0\u1edbc 1:<\/b> Ph\u00e2n t\u00edch v\u1ebf tr\u00e1i th\u00e0nh nh\u00e2n t\u1eed b\u1eb1ng c\u00e1ch nh\u00f3m:<br\/> $(x+2)(x+5)(x+3)(x+4)-24= \\left( {{x}^{2}}+7x+10 \\right)\\left( {{x}^{2}}+7x+12 \\right)-24$.<br\/> <b> B\u01b0\u1edbc 2:<\/b> \u0110\u1eb7t ${{x}^{2}}+7x+11=t$, ph\u00e2n t\u00edch th\u00e0nh nh\u00e2n t\u1eed theo $t $ b\u1eb1ng c\u00e1ch d\u00f9ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c.<br\/> <b> B\u01b0\u1edbc 3: <\/b> N\u1ebfu $a.b = 0$ th\u00ec $a = 0$ ho\u1eb7c $b = 0$. <br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/> Ta c\u00f3:<br\/> $\\begin{aligned} & (x+2)(x+3)(x+4)(x+5)-24=0 \\\\ &\\Leftrightarrow (x+2)(x+5)(x+3)(x+4)-24=0 \\\\ & \\Leftrightarrow \\left( {{x}^{2}}+7x+10 \\right)\\left( {{x}^{2}}+7x+12 \\right)-24=0 \\\\ & \\text{\u0110\u1eb7t }\\,\\,{{x}^{2}}+7x+11=t \\\\ & \\Rightarrow \\left( t+1 \\right)\\left( t-1 \\right)-24=0 \\\\ &\\Leftrightarrow {{t}^{2}}-1-24=0 \\\\ & \\Leftrightarrow{{t}^{2}}-25=0 \\\\ & \\Leftrightarrow \\left( t+5 \\right)\\left( t-5 \\right)=0 \\\\ & \\Rightarrow \\left[ \\begin{aligned} & t+5=0 \\\\ & t-5=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left[ \\begin{aligned} & t=-5 \\\\ & t=5 \\\\ \\end{aligned} \\right. \\\\ & \\text{Thay l\u1ea1i }\\,\\,\\left[ \\begin{aligned} & {{x}^{2}}+7x+11=-5 \\\\ & {{x}^{2}}+7x+11=5 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left[ \\begin{aligned} & {{x}^{2}}+7x+16=0 \\\\ & {{x}^{2}}+7x+6=0 \\\\ \\end{aligned} \\right.\\Leftrightarrow \\left[ \\begin{aligned} & x=\\varnothing \\\\ & \\left( x+1 \\right)\\left( x+6 \\right)=0 \\\\ \\end{aligned} \\right.\\\\& \\Rightarrow \\left[ \\begin{aligned} & x=-1 \\\\ & x=-6 \\\\ \\end{aligned} \\right. \\\\ \\end{aligned}$. <br\/> <span class='basic_pink'> Do \u0111\u00f3 ph\u1ea3i \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $-1 v\u00e0 - 6$ <\/span><\/span> "}]}],"id_ques":627},{"time":24,"part":[{"title":"\u0110i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng trong k\u1ebft qu\u1ea3 ph\u00e2n t\u00edch \u0111a th\u1ee9c th\u00e0nh nh\u00e2n t\u1eed","title_trans":"","temp":"fill_the_blank_random","correct":[[["x+1","1+x"],["x+2","2+x"]]],"list":[{"point":10,"width":40,"type_input":"","ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/4.jpg' \/><\/center> $x^3+5x^2+8x+4$$=(\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})\\times (\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{})^2$","hint":"Nh\u1eadn th\u1ea5y t\u1ed5ng c\u00e1c h\u1ec7 s\u1ed1 c\u1ee7a l\u0169y th\u1eeba b\u1eadc l\u1ebb b\u1eb1ng t\u1ed5ng c\u00e1c h\u1ec7 s\u1ed1 l\u0169y th\u1eeba b\u1eadc ch\u1eb5n n\u00ean \u0111a th\u1ee9c c\u00f3 m\u1ed9t nghi\u1ec7m b\u1eb1ng $-1$. Khi \u0111\u00f3 \u0111a th\u1ee9c c\u00f3 m\u1ed9t nh\u00e2n t\u1eed l\u00e0 $x + 1$. Ta d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch r\u1ed3i nh\u00f3m sao cho xu\u1ea5t hi\u1ec7n nh\u00e2n t\u1eed $x + 1$. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/><b> B\u01b0\u1edbc 1:<\/b> Ta ph\u00e2n t\u00edch b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch r\u1ed3i nh\u00f3m:<br\/> $x^3+5x^2+8x+4 $$=x^3+x^2+4x^2+4x+4x+4$.<br\/> <b> B\u01b0\u1edbc 2:<\/b> Ph\u00e2n t\u00edch ti\u1ebfp theo ph\u01b0\u01a1ng ph\u00e1p \u0111\u1eb7t nh\u00e2n t\u1eed chung. <br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3:<br\/> $\\begin{align} & x^3+5x^2+8x+4 \\\\ & =x^3+x^2+4x^2+4x+4x+4 \\\\ & = (x^3+x^2)+(4x^2+4x)+(4x+4)\\\\ & =x^2(x+1)+4x(x+1)+4(x+1) \\\\ & =(x+1)(x^2+4x+4) \\\\ & =(x+1)(x+2)^2 \\\\ \\end{align}$.<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $x + 1$ v\u00e0 $x + 2$.<\/span>"}]}],"id_ques":628},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/2.jpg' \/><\/center> Ph\u00e2n t\u00edch \u0111a th\u1ee9c $ab(a+b)-bc(b+c)+ca(a+c)+abc$ th\u00e0nh nh\u00e2n t\u1eed, ta \u0111\u01b0\u1ee3c:","select":["A. $(a+b+c)(ab+ac+bc)$ ","B. $(a+b+c)(ab+ac-bc)$ ","C. $(a+b+c)(a+b)$","D. $(a+b)(a+c)(b+c)$"],"hint":" Nh\u00e2n ra v\u00e0 nh\u00f3m, th\u00eam b\u1edbt abc: $\\left( {{a}^{2}}b+a{{b}^{2}}+abc \\right)$$-\\left( {{b}^{2}}c+b{{c}^{2}}+abc \\right)$$+\\left( a{{c}^{2}}+{{a}^{2}}c+abc \\right)$<br\/> \u0110\u1eb7t nh\u00e2n t\u1eed chung \u0111\u1ec3 ph\u00e2n t\u00edch.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b> B\u01b0\u1edbc 1:<\/b> Nh\u00e2n ra v\u00e0 nh\u00f3m, th\u00eam b\u1edbt abc \u0111\u1ec3 \u0111\u01b0\u1ee3c: $\\left( {{a}^{2}}b+a{{b}^{2}}+abc \\right)$$-\\left( {{b}^{2}}c+b{{c}^{2}}+abc \\right)$$+\\left( a{{c}^{2}}+{{a}^{2}}c+abc \\right)$ <br\/> <b> B\u01b0\u1edbc 2:<\/b> \u0110\u1eb7t nh\u00e2n t\u1eed chung \u0111\u1ec3 ph\u00e2n t\u00edch.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3:<br\/>$ ab(a+b)-bc(b+c)+ca(a+c)+abc $<br\/>$ ={{a}^{2}}b+a{{b}^{2}}-{{b}^{2}}c-b{{c}^{2}}$$+{{a}^{2}}c+a{{c}^{2}}+abc $<br\/>$ =\\left( {{a}^{2}}b+a{{b}^{2}}+abc \\right)-\\left( {{b}^{2}}c+b{{c}^{2}}+abc \\right)$$+\\left( a{{c}^{2}}+{{a}^{2}}c+abc \\right) $<br\/>$ =ab\\left( a+b+c \\right)-bc\\left( b+c+a \\right)$$+ac\\left( c+a+b \\right) $<br\/>$ =\\left( a+b+c \\right)\\left( ab+ac-bc \\right) $ <span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":2}]}],"id_ques":629},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai7/lv3/img\/3.jpg' \/><\/center> Ph\u00e2n t\u00edch \u0111a th\u1ee9c $x^3-x^2-14x+24$ th\u00e0nh nh\u00e2n t\u1eed, ta \u0111\u01b0\u1ee3c:","select":["A. $(x+2)(x+3)(x-4)$ ","B. $(x+2)(x-3)(x-4)$ ","C. $(x-2)(x-3)(x+4)$","D. $(x-2)(x+3)(x+4)$"],"hint":" S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch v\u00e0 \u0111\u1eb7t nh\u00e2n t\u1eed chung \u0111\u1ec3 ph\u00e2n t\u00edch.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/> <b> B\u01b0\u1edbc 1:<\/b> S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p t\u00e1ch \u0111\u1ec3 ph\u00e2n t\u00edch: ${{x}^{3}}-2{{x}^{2}}+{{x}^{2}}-2x-12x+24$ <br\/> <b> B\u01b0\u1edbc 2:<\/b> \u0110\u1eb7t nh\u00e2n t\u1eed chung \u0111\u1ec3 ph\u00e2n t\u00edch.<br\/><span class='basic_green'>Gi\u1ea3i<\/span><br\/><span class='basic_left'>Ta c\u00f3:<br\/>$\\begin{align} & {{x}^{3}}-{{x}^{2}}-14x+24 \\\\ & ={{x}^{3}}-2{{x}^{2}}+{{x}^{2}}-2x-12x+24 \\\\ & =\\left( {{x}^{3}}-2{{x}^{2}} \\right)+\\left( {{x}^{2}}-2x \\right)-\\left( 12x-24 \\right) \\\\ & ={{x}^{2}}\\left( x-2 \\right)+x\\left( x-2 \\right)-12\\left( x-2 \\right) \\\\ & =\\left( x-2 \\right)\\left( {{x}^{2}}+x-12 \\right) \\\\ & =\\left( x-2 \\right)\\left( {{x}^{2}}+4x-3x-12 \\right) \\\\ & =\\left( x-2 \\right)\\left[ x\\left( x+4 \\right)-3\\left( x+4 \\right) \\right] \\\\ & =\\left( x-2 \\right)\\left( x+4 \\right)\\left( x-3 \\right) \\\\ \\end{align}$.<span><br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C.<\/span>","column":2}]}],"id_ques":630}],"lesson":{"save":0,"level":3}}