Factorise the following polynomial: x^3 + x^2 - 4x -4
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Answer:
=(x+1)(x–2)(x+2)
Step-by-step explanation:
Let f(x)=x
3
+x
2
–4x–4
For x=−1, the value of f(x) will be
f(−1)=(−1)
3
+(−1)
2
–4(−1)–4
=−1+1+4–4=0
As, f(−1)=0 so (x+1) is a factor of f(x).
Now, performing long division we have
Thus, f(x)=(x+1)(x
2
–4)
=(x+1)(x–2)(x+2)
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