Question

If x + 2 and x − 1 are the factors of x³ + 10x² + mx + n, then the values of m and n are respectively

(a) 5 and −3

(b) 17 and −8

(c) 7 and −18

(d) 23 and −19

Answer 1

It is given and are the factors of the polynomial

i.e., and

Now

$$\begin{gathered} -8+40-2m+n=0 \\ \Rightarrow -2m+n=-32 \\ \Rightarrow 2m-n=32...\left(i\right) \end{gathered}$$

And

Solving equation (i) and (ii) we get

m = 7 and n = − 18

Hence, the correct option is (c)