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KT
9 tháng 8 2018
mk ghi đáp án, còn lại bạn tự biến đổi
a) \(2x^3-x^2+5x+3=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(x^3+5x^2+8x+4=\left(x+1\right)\left(x+2\right)^2\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
d) \(4x^4+1=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)
e) \(x^4-7x^3+14x^2-7x+1=\left(x^2-4x+1\right)\left(x^2-3x+1\right)\)
KT
9 tháng 8 2018
mk làm chi tiết theo yêu của của người hỏi đề:
a) \(2x^3-x^2+5x+3\)
\(=\left(2x^3-2x^2+6x\right)+\left(x^2-x+3\right)\)
\(=2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
b) \(x^3+5x^2+8x+4\)
\(=\left(x^3+4x^2+4x\right)+\left(x^2+4x+4\right)\)
\(=x\left(x^2+4x+4\right)+\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x^2+4x+4\right)\)
\(=\left(x+1\right)\left(x+2\right)^2\)
26 tháng 9 2018
\(x^3-x^2-14x+24\)
\(=x^3-2x^2+x^2-2x-12x+24\)
\(=x^2\left(x-2\right)+x\left(x-2\right)-12\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-2\right).\left[x^2+4x-3x-12\right]\)
\(=\left(x-2\right).\left[x\left(x+4\right)-3\left(x+4\right)\right]\)
\(=\left(x-2\right)\left(x+4\right)\left(x-3\right)\)
\(x^4+x^3+2x-4\)
\(=x^4-x^3+2x^3-2x^2+2x^2-2x+4x-4\)
\(=x^3\left(x-1\right)+2x^2\left(x-1\right)+2x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+2x+4\right)\)
\(=\left(x-1\right).\left[x^2\left(x+2\right)+2\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+2\right)\)
\(8x^4-2x^3-3x^2-2x-1\)
\(=8x^4-8x^3+6x^3-6x^2+3x^2-3x+x-1\)
\(=8x^3\left(x-1\right)+6x^2\left(x-1\right)+3x\left(x-1\right)+x-1\)
\(=\left(x-1\right)\left(8x^3+6x^2+3x+1\right)\)
\(=\left(x-1\right)\left[\left(8x^3+1\right)+\left(6x^2+3x\right)\right]\)
\(=\left(x-1\right)\left[\left(2x+1\right)\left(4x^2-2x+1\right)+3x\left(2x+1\right)\right]\)
\(=\left(x-1\right)\left(2x+1\right)\left(4x^2+x+1\right)\)
\(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
Chúc bạn học tốt.
NN
0
16 tháng 9 2016
A/ \(2x^2+7x+5=2\left(x^2+2x+1\right)+3x+3=2\left(x+1\right)^2+3\left(x+1\right)\)
\(=\left(x+1\right)\left(2x+5\right)\)
B/ \(x^2-4x-5=\left(x^2-4x+4\right)-9=\left(x-2\right)^2-3^2=\left(x-5\right)\left(x+1\right)\)
C/ \(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
D/\(x^4+4x^2-5=\left(x^4+4x^2+4\right)-9=\left(x^2+2\right)^2-3^2=\left(x^2-1\right)\left(x^2+5\right)=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
16 tháng 9 2016
a) = 2x^2 + 2x +5x + 5 = 2x(x+1) + 5(x+1) = (2x+5)(x+1)
b) = x^2 + x - 5x - 5 = x(x-1) - 5(x-1) = (x-5)(x-1)
c) = x^3 ( x+1) + x+1 = (x^3+1) (x+1) = (x+1)^2 * (x^2 - x +1)
d) = x^4 - x^2 + 5x^2 -5 = x^2 (x^2-1) + 5(x^2-1) = (x^2+5)(x-1)(x+1)
CM
1
FM
12 tháng 10 2018
Ta có:
\(2x^2-5xy+3y^2\)
\(=2x^2-2xy-3xy+3y^2=2x\left(x-y\right)-3y\left(x-y\right)\)
\(=\left(x-y\right)\left(2x-3y\right)\)
\(x^3-7x-6=x^3+1-7x-7\)
\(=\left(x+1\right)\left(x^2-x+1\right)-7\left(x+1\right)=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x-3\right)\left(x+2\right)\)
HP
1 tháng 10 2016
b)x3-7x+6=x3-x-6x+6=x(x2-1)-6(x-1)=x(x-1)(x+1)-6(x-1)
=(x-1)[x(x+1)-6]=(x-1)(x2+x-6)=(x-1)(x2+3x-2x-6)=(x-1)[x(x+3)-2(x+3)]=(x-1)(x-2)(x+3)
c)x3-x2-x-2
=x3-2x2+x2-2x+x-2
=x2(x-2)+x(x-2)+(x-2)
=(x-2)(x2+x+1)
3 tháng 9 2018
\(x^3-7x+6\)
\(=x^3-x^2+x^2-x-6x+6\)
\(=x^2\left(x-1\right)+x\left(x-1\right)-6\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x-6\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x+3\right)\)
có đề = \(\left(x^4+2x^3+5x^2\right)-\left(x^3+2x^2+5x\right)-\left(x^2+2x+5\right)=x^2\left(x^2+2x+5\right)-x\left(x^2+2x+5\right)-\left(x^2+2x+5\right)=\left(x^2-x-1\right)\left(x^2+2x+5\right)\)