Question:
(x + 1) is a factor of the polynomial
(a) $x^{3}+x^{2}-x+1$
(b) $x^{3}+2 x^{2}-x-2$
(c) $x^{3}+2 x^{2}-x+2$
(d) $x^{4}+x^{3}+x^{2}+1$
Solution:
(b) $x^{3}-2 x^{2}-x-2$
Let:
$f(x)=x^{3}-2 x^{2}-x-2$
By the factor theorem, (x + 1) will be a factor of f(x) if f (
We have:
$f(-1)=(-1)^{3}+2 \times(-1)^{2}-(-1)-2$
$=-1+2+1-2$
$=0$
Hence, $(x+1)$ is a factor of $f(x)=x^{3}+2 x^{2}-x-2$.
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