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Question
Factorise the following polynomials using synthetic division:
2x3 – 3x2 – 3x + 2
Solution
p(x) = 2x3 – 3x2 – 3x + 2
p(1) = 2(1)3 – 3(1)2 – 3(1) + 2
= 2 – 3 – 3 + 2
= 2 – 6
= – 4
≠ 0
x – 1 is not a factor
p(–1) = 2(–1)3 – 3(–1)2 – 3(–1) + 2
= – 2 – 3 + 3 + 2
= 5 – 5
= 0
∴ x + 1 is a factor
2x2 – 5x + 2 = 2x2 – 4x – x + 2
= 2x(x – 2) – 1(x – 2)
= (x – 2)(2x – 1)
∴ The factors of 2x3 – 3x2 – 3x + 2 = (x + 1)(x – 2)(2x – 1)
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