Question

Find the factors of f(x), given that x = 4 is a zero.f(x) = x3 − 7x2 + 2x + 40.

Answer 1

Answer:

Explanation:

Here, we want to get the factors of the given polynomial

From what we have:

$\begin{gathered} x\text{ = 4} \\ \text{ Then x-4 is a factor} \end{gathered}$

To get other factors, we have to divide the polynomial by the first factor obtained

Mathematically, we have that as follows:

$\frac{x^3-7x^2\text{ + 2x +40}}{x-4}=x^2-9x\text{ + 20}$

What we finally have to do is to factorize what was obtained

We have that as:

$\begin{gathered} x^2-9x+20=x^2-4x-5x+20 \\ =x(x-4)-5(x-4) \\ =\text{ (x-5)(x-4)} \end{gathered}$

So, we have the factors as (x-5)(x-4)(x-4)