Determine which of the following polynomials has $(x + 1)$ a factor :
$x^{4} + x^{3} + x^{2} + x + 1$

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Solution

We have,
$x^{4} + x^{3} + x^{2} + x + 1$
$x + 1 = 0$
$x = - 1$
Replace x by $- 1$ we get,
$= x^{4} + x^{3} + x^{2} + x + 1$
$= (- 1)^{4} + (- 1)^{3} + (- 1)^{2} + (- 1) + 1$
$= 1 - 1 + 1 - 1 + 1$
$= 1$
Hence, this is answer.

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Similar questions

Determine which of the following polynomials has (x+1) as a factor:
(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^{4} + x^{3} + x^{2} + x + 1

(x + 1)

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

Determine which of the following polynomials has (x + 1) a factor:

(i) x³ + x² + x + 1 (ii) x⁴ + x³ + x² + x + 1

(iii) x⁴ + 3x³ + 3x² + x + 1 (iv)

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