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

A. 9

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`