Question

Given the function
P
(
x
)
=
x
3
+
4
x
2
+
k
x
+
15
,
for what value of k is
(
x
+
3
)
a factor of
P
(
x
)
?


−
26


−
8


8


26

Answer 1

If (x + 3) is a factor, then P(-3) = 0.

P(-3) = (-3)^3 + 4(-3)^2 + k(-3) + 15 = -27 + 36 - 3k + 15 = 24 - 3k.

Set 24 - 3k = 0 ⇒ 3k = 24 ⇒ k = 8.

Answer: 8.