Question

For \[f(x)=3x^4+4x^3-12x^2+12\], which is the correct factorization of \[f'(x)\]?

Options

• \[12(x-1)(x+2)\]

• \[12x(x+1)(x-2)\]

• \[12x(x-1)(x+2)\]

• \[24x(x-1)(x+2)\]

Answer 1

Factoring \[12x\] from \[12x^3+12x^2-24x\] gives \[12x(x^2+x-2)\]. Since \[x^2+x-2=(x-1)(x+2)\], the stated factorization follows.