In each of the following two polynomials, find the values of $a$, if $x - a$ is a factor:$x^5 - a^2x^3 + 2x + a + 1$

Given:

Given expression is $x^5 - a^2x^3 + 2x + a + 1$.

$x - a$ is a factor of $x^5 - a^2x^3 + 2x + a + 1$.

To do:

We have to find the value of $a$.

Solution:

We know that,

If $(x-m)$ is a root of $f(x)$ then $f(m)=0$.

Therefore,

$f(a)=0$

$\Rightarrow (a)^5 - a^2(a)^3 + 2(a)+a + 1=0$

$\Rightarrow a^5-a^5+3a+1=0$

$\Rightarrow 3a+1=0$

$\Rightarrow 3a=-1$

$\Rightarrow a=\frac{-1}{3}$

The value of $a$ is $\frac{-1}{3}$.   

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Updated on: 10-Oct-2022

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