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Question
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
Solution
By remainder theorem we know that when a polynomial f(x) is divided by x – a, then the remainder is f(a).
Let f(x) = 2x3 + 3x2 – 5x – 6
f(–2) = 2(–2)3 + 3(–2)2 – 5(–2) – 6
= –16 + 12 + 10 – 6
= 0
Thus, (x + 2) is a factor of the polynomial f(x).
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