Check whether $x + 1$ is a factor of $x^{4} + x^{3} + x^{2} + x + 1$ .

True

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False

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Solution

The correct option is B False
The zero of $x + 1$ is $- 1$
Let $p (x) = x^{4} + x^{3} + x^{2} + x + 1$
Then, $p (- 1) = (- 1)^{4} + (- 1)^{3} + (- 1)^{2} + (- 1) + 1$
$= 1 - 1 + 1 - 1 + 1 = 1$
Since, $p (- 1) \neq 0$
Therefore, by Factor theorem, $x + 1$ is not a factor of $x^{4} + x^{3} + x^{2} + x + 1$

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Similar questions

Q. Check whether

x + 1

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Now in each of the pairs of polynomials given below, check whether the first is a factor of the second:

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(ii) x − 1, x³ + 1

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(v) x − 1, x⁴ − 1

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Q. Check whether the following polynomial has

(x + 1)

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

Q. x + 1 is a factor of the polynomial
(a) x³ + x²– x + 1
(b) x³ + x² + x + 1
(c) x⁴ + x³ + x² + 1
(d) x⁴ + 3x³ + 3x² + x + 1

$x + 1$ is a factor of the polynomial
$A .$ $x^{3} + x^{2} - x + 1$
$B .$ $x^{3} + x^{2} + x + 1$
$C .$ $x^{4} + x^{3} + x^{2} + 1$
$D .$ $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

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Check whether x+1 is a factor of x4+x3+x2+x+1.

The correct option is B FalseThe zero of x+1 is −1Let p(x)=x4+x3+x2+x+1Then, p(−1)=(−1)4+(−1)3+(−1)2+(−1)+1 =1−1+1−1+1=1Since, p(−1)≠0Therefore, by Factor theorem, x+1 is not a factor of x4+x3+x2+x+1

Check whether $x + 1$ is a factor of $x^{4} + x^{3} + x^{2} + x + 1$ .