Question

Find the value of a such that (x − 4) is a factors of 5x³ − 7x² − ax − 28.

Answer 1

Let be the given polynomial.

By the factor theorem,

(x − 4) is a factor of f(x).

Therefore f(4) = 0

Hence ,

$$\begin{gathered} \Rightarrow 320-112-4a-28=0 \\ \Rightarrow 180-4a=0 \\ \Rightarrow a=\frac{180}{4}=45 \end{gathered}$$

Hence,