Question

1. What would s have to be so that x^3+ 5x^2 + sx + 6 is divisible by (x+2)?

A. 9
B. 5
C. 2
D. -6
E. -13

Answer 1

Answer:

A. 9

Step-by-step explanation:

We use the remainder theorem.

The given function is

$f(x) = {x}^{3} + 5 {x}^{2} + sx + 6$

If this function is divisible by x+2, then by the remainder theorem,

$f( - 2) = 0$

This implies that;

${( - 2)}^{3} + 5( - 2 )^{2} + s( - 2) + 6 = 0$

We evaluate to get:

$- 8 + 20 - 2s + 6 = 0$

$18 - 2s = 0$

$2s = 18 \\ s = 9$