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Question
Using the Reminder Theorem, factorise of the following completely.
2x3 + x2 – 13x + 6
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Solution
Let f (x) = 2x3 + x2 − 13x + 6
For x = 2,
f(x) = f(2) = 2(2)3 + (2)2 − 13(2) + 6 = 16 + 4 − 26 + 6 = 0
Hence, (x − 2) is a factor of f(x).
∴ `2x^3 + x^2 - 13x + 6 = (x-2) (2x^2 + 5x -3)`
= `(x-2)(2x^2 + 6x -x -3)`
= `(x-2) [2x(x + 3) -(x-3)]`
=` (x - 2)(x + 3) (2x - 1)`
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