Question

given polynomials f(x) and a factor of f(x), factor f(x) completely. f (x) = 2x3 – 3x² – 8x – 3; (x – 3)

Answer 1

Answer: Given that the following is the factor of f(x), we then have.

$\begin{gathered} (x-3)y=f(x) \\ \therefore\rightarrow \\ y=\frac{f(x)}{(x-3)}=\frac{2x^3-3x^2-8x-3}{(x-3)} \end{gathered}$

By algebraic long division, we then have the following.

$y=2x^2+3x+1$

Which can be further factorized as:

$2x^2+3x+1=(2x+1)(x+1)$

Therefore the complete factorization of f(x) is as follows:

$f(x)=(2x+1)(x+1)((x-3)=2x^3-3x^2-8x-3$