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Question
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
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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(1/2) = 2(1/2)^3 + 3(1/2)^2 - 5(1/2) - 6`
= `1/4 + 3/4 - 5/2 - 6`
= `-5/2 - 5`
= `(-15)/2 ≠ 0`
Thus, (2x – 1) is not a factor of the polynomial f(x).
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