Question

Phân tích đa thức thành nhân tử

1,(x^2+x)^2+4x^2+4x-12

2,(x^2+x+1)(x^2+x+2)-12

3,(x+1)(x+2)(x+3)(x+4)-24

Answer 1

Làmmmm

1)\(\left(x^2+x\right)^2+4x^2+4x-12\)

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

\(=a^2+4a-12\)

\(=\left(a-2\right)\left(a+6\right)\)

\(=\left(x^2+x-2\right)\left(x^2+x+6\right)\)

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

Answer 2

2) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)

\(=\left(a+1\right)\left(a+2\right)-12\)

\(=a^2+3a+2-12=a^2+3a-10\)

\(=\left(a-2\right)\left(a+5\right)\)

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

=\(\left(x-1\right)\left(x+2\right)\left(x^2+x+5\right)\)

Answer 3

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)

\(=\left(x^2+5x+5\right)^2-1-24\)

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

\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)

\(=x\left(x+5\right)\left(x^2+5x+10\right)\)