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Question
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
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Solution
f(x) = x3 + x2 – 4x – 4
For x = –1,
f(x) = f(–1)
= (–1)3 + (–1)2 – 4(–1) – 4
= –1 + 1 + 4 – 4
= 0
Hence, (x + 1) is a factor of f(x).
x2 – 4
`x + 1")"overline(x^3 + x^2 - 4x - 4)`
x3 + x2
– –
– 4x – 4
– 4x – 4
+ +
0
∴ x3 + x2 – 4x – 4 = (x + 1)(x2 – 4)
= (x + 1)[(x)2 – (2)2]
= (x + 1)(x + 2)(x – 2)
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