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Question
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
Solution
f(x) = 4x3 + 4x2 – 9x – 9
Let x = -1, then
f(-1) = 4 (-1)3 + 4 (-1)2 – 9 (-1) – 9
= 4(–1) + 4(1) + 9 – 9
= –4 + 4 + 9 – 9
= 13 – 13
= 0
∴ (x + 1) is a factor of f(x)
Now dividing f(x) by x + 1, we get
f(x) = 4x3 + 4x2 – 9x – 9
= (x + 1)(4x2 – 9)
= (x + 1){(2x)2 – (3)2}
= (x + 1)(2x + 3)(2x – 3)
`x + 1")"overline(4x^3 + 4x^2 - 9x - 9)("4x^2 - 9`
4x3 + 4x2
– –
– 9x – 9
– 9x – 9
+ +
x
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