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Question
Factorise the following polynomials using synthetic division:
x3 – 7x + 6
Solution
p(x) = x3 – 7x + 6
p(1) = 13 – 7(1) + 6
= 1 – 7 + 6
= 7 – 7
= 0
∴ x – 1 is a factor
x2 + x – 6 = x2 + 3x – 2x – 6
= x(x + 3) – 2(x + 3)
= (x + 3)(x – 2)
This (x – 1)(x – 2)(x + 3) are factors.
∴ x3 – 7x + 6 = (x – 1)(x – 2)(x + 3)
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