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Question
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
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Solution
p(x) = 2x3 − x2 − 45
Divisor = q(x) = x − 3
∴ Let x = 3
∴ p(3) = 2 × (3)3 − (3)2 − 45
= 2 × 27 − 9 − 45
= 54 − 54
= 0
So, by factor theorem q(x) = x − 3 is a factor of polynomial p(x) = 2x3 − x2 − 45.
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