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Question
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
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Solution
x3 + x2 - 4x - 4
Let x + 1 = 0
∴ x = -1
On substituting value of x in the expression
∴ f(-1) = (-1)3 + (-1)2 - 4(-1) -4 = 0
Clearly x + 1 is a factor of
f(x) = x3 + x2 - 4x - 4
∴ f(x) = (x + 1) (x2 - 4) ...(By actual division)
= (x + 1) (x - 2) (x + 2)
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