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Question
Factorise the following polynomials using synthetic division:
x3 – 10x2 – x + 10
Solution
p(x) = x3 – 10x2 – x + 10
= 1 – 10 – 1 + 10
= 11 – 11
= 0
∴ x – 1 is a factor
x2 – 9x – 10 = x2 – 10x + x – 10
= x(x – 10) + 1(x – 10)
= (x – 10)(x + 1)
This (x – 1)(x + 1)(x – 10) are the factors.
∴ x3 – 10x2 – x + 10 = (x – 1)(x – 10)(x + 1)
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