Question

Phân tích đa thức sau thành nhân tử:(đặt biến phụ)

a) ( x² +4x + 8)² + 3x( x² + 4x + 8) + 2x²

b) ( x²+ x+1).( x² + x+2) - 12

c) (x² + 8x +7).(x² + 8x +15) + 15

d)(x+2)(x+3)(X+4)(x+5) - 24

Answer 1

a, Đặt \(x^2+4x+8=a,x=b\)

\(\left(a\right)\)\(\Leftrightarrow a^2+3ab+2b^2\)\(=\)\(\left(a+b\right)\left(a+2b\right)\)\(=\left(x^2+5x+8\right)\left(x^2+6x+8\right)\)

b, Đặt \(x^2+x+1=t\)

\(\left(b\right)=t.\left(t+1\right)-12=t^2+t-12\)\(=\left(t-3\right)\left(t+4\right)\)

\(=\left(x^2+x-2\right)\left(x^2+x+5\right)\)

c, Tương tự câu b

d,

\(\left(d\right)=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

Đặt \(x^2+7x+10=t\)

\(\left(d\right)=t\left(t+2\right)-24=t^2+2t-24=\left(t-4\right)\left(t+6\right)\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)