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Question
Factorise the following polynomials using synthetic division:
– 7x + 3 + 4x3
Solution
p(x) = – 7x + 3 + 4x3
= 4x3 – 7x + 3
p(1) = 4(1)3 – 7(1) + 3
= 4 – 7 + 3
= 7 – 7
= 0
∴ x – 1 is a factor
4x2 + 4x – 3 = 4x2 + 6x – 2x – 3
= 2x(2x + 3) – 1(2x + 3)
= (2x + 3)(2x – 1)
∴ The factors of – 7x + 3 + 4x3 = (x – 1)(2x + 3)(2x – 1)
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