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Question
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial completely.
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Solution
`f(x) = x^3 + x^2 - 4x - 4`
Let x - 2 = 0, then x = 2
`therefore f(2) = (2)^3 +(2)^2 - 4 (2)-4`
f (2) = 8 + 4 - 8 - 4
f (2) = 0
∴ x - 2 is a factor of f (x)
Now dividing x3 + x2 - 4x - 4 by x - 2, we get
`=x^3 +x^2 - 4x +4 = (x-2)(x^2 + 3x + 2)`
= (x - 2) (x + 2) (x + 1 )
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