Find whether $x+7$ is he factor of $x^2 - 5x + 84$.

Given :

The given polynomials are,  $f(x) =  x^2 - 5x + 84$ and  $g(x) = x+7 = x-(-7)$

To do :

We have to find whether $g(x)$ is the factor of $f(x)$.

Solution :

According to factor theorem, if $f(x)$ is a polynomial of degree n ≥ 1 and 'a' is any real number, then,$ (x-a)$ is a factor of $f(x)$, if $f(a)=0$.

Therefore,

$g(x)$ is a factor of $f(x)$ if $f(-7) = 0$.

$f(-7) = (-7)^2-5(-7)+84$

         $= 49+35+84$

         $= 168$

$f(-7)$ is not equal to zero.

Therefore, $x+7$ is not a factor of  $x^2 - 5x + 84$.

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Updated on: 10-Oct-2022

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