How do you use the remainder theorem to see if the $x+6$ is a factor of $x^5+6x^4-3x^2-22x-29$ ?

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Answer 1 · 2017-02-17T10:33:46

See explanation.

According to the Reminder theorem to see if $(x-a)$ is a factor of a polynomial $P(x)$ you have to check if $P(a)=0$

In the given example we have:

$P(x)=x^5+6x^4-3x^2-22x-29$ and $a=-6$ , so:

$P(-6)=(-6)^5+6*(-6)^4-3*(-6)^2-22*(-6)-29$

$=-7776+7776-108+132-29=132-108-29=$

$=24-29=-5$

The value $P(-6)$ is different from zero, so the polynomial is not divisible by $(x+6)$

How do you use the remainder theorem to see if the x+6x+6 is a factor of x^5+6x^4-3x^2-22x-29x^5+6x^4-3x^2-22x-29?