Foundation
Mathematics Foundation
Factor theorem
Question
If (x + 5) is a factor of p(x) = x3 – 20x + 5k then k = ?
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Solution
If (x + 5) is a factor of p(x), then by the Factor Theorem, p(– 5) = 0. We substitute x = – 5 into the polynomial and solve for k.
p(x) = x3 − 20x + 5k
p(– 5) = (− 5)3 − 20(− 5) + 5k = 0
− 125 + 100 + 5k = 0
− 25 + 5k = 0
5k = 25
k = 5
Final Answer: 5