Determine $(x + 1)$ is a factor of $x^{3} + x^{2} + x + 1$ or not.

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Solution

Applying remainder theorem, we get
$x + 1 = 0$
$x = - 1$

Now,
$x^{3} + x^{2} + x + 1$

Replacing $x$ with $- 1$ , we get
$= (- 1)^{3} + (- 1)^{2} + (- 1) + 1$
$= - 1 + 1 - 1 + 1$
$= 0$

Hence, $(x + 1)$ is a factor of polynomial $(x^{3} + x^{2} + x + 1) .$

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Similar questions

Determine which of the following polynomials have $(x + 1)$ as a factor: [2 MARKS]
(i) $x^{3} + x^{2} + x + 1$
(ii) $x^{4} + x^{3} + x^{2} + x + 1$

(x + 1)

x^{3} + x^{2} + x + 1

(x + 1)

x^{4} - x^{3} + x^{2} - x + 1

p (x) = x^{3} - x^{2} - x - 1, q (x) = x - 1

p (x) = 2 x^{3} - x^{2} - 45, q (x) = x - 3

(x + 1)

x^{3} + x^{2} + x + 1

x^{4} + x^{3} + x^{2} + x + 1

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