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Question
Find the value of p if x3 + 2x2 − 6x + p is exactly divisible by x + 4.
Sum
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Solution
Let f(x) = x3 + 2x2 − 6x + p
Let x + 4 = 0
x = −4
f(−4) = 0
⇒ f(−4) = (−4)3 + 2(−4)2 − 6(−4) + p = 0
⇒ −64 + 32 + 24 + p = 0
⇒ −8 + p = 0
⇒ p = 8
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