Question:
$x+1$ is a factor of the polynomial
(a) $x^{3}+x^{2}-x+1$
(b) $x^{3}+x^{2}+x+1$
(c) $x^{4}+x^{3}+x^{2}+1$
(d) $x^{4}+3 x^{3}+3 x^{2}+x+1$
Solution:
(b) Let assume (x + 1) is a factor of x3 + x2 + x+1.
So, x = -1 is zero of x3 + x2 + x+1
(-1)3 + (-1)2 + (-1) + 1 = 0 => -1+1-1 + 1 = 0 => 0 = 0 Hence, our assumption is true.
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