Question

Phân tích đa thức thàn nhân tử :

a) x⁴-7x³+14x²-7x+1

b)x⁴+6x³+7x²-6x+1

c)x(x+4)(x+6)(x+10)+128

Bạn nào giúp được mình k T.T

Answer 1

b)\(x^4+6x^3+7x^2-6x+1=x^4+6x^3-2x^2+9x^2-6x+1\)

=\(x^4+\left(6x^3-2x^2\right)+\left(9x^2-6x+1\right)\)

\(=\left(x^2\right)^2-2x^2\left(3x-1\right)+\left(3x-1\right)^2\)

\(=\left(x^2+3x-1\right)^2\)

c)\(x\left(x+4\right)\left(x+6\right)\left(x+10\right)+128\)

\(=\left(x^2+10x\right)\left(x^2+10x+24\right)+128\)

đặt \(x^2+10x+12=z\)

\(=\left(z-12\right)\left(z+12\right)+128=z^2-144+128\)

\(=z^2-16=\left(z-4\right)\left(z+4\right)\)\(=\left(x^2+10x-4+12\right)\left(x^2+10x+4+12\right)\)

\(=\left(x^2+10x+8\right)\left(x^2+10x+16\right)\)

\(=\left(x^2+10x+8\right)\left(x^2+2x+8x+16\right)\)

\(=\left(x^2+10x+8\right)\left[x\left(x+2\right)+8\left(x+2\right)\right]\)

\(=\left(x^2+10x+8\right)\left(x+2\right)\left(x+8\right)\)

Answer 2

a: =x^4-4x^3+x^2-3x^3+12x^2-3x+x^2-4x+1

=(x^2-4x+1)(x^2-3x+1)

c: =(x^2+10x)(x^2+10x+24)+128

=(x^2+10x)^2+24(x^2+10x)+128

=(x^2+10x+16)(x^2+10x+8)

=(x^2+10x+8)(x+2)(x+8)