Question

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22

Answer 1

Answer:

$x-2$ is not a factor of $p(x)=4x^2-3x+22$.

Step-by-step explanation:

According to the factor theorem, if $x-a$ is a factor of $p(x)$, then $p(a)=0$.

Let $p(x)=4x^2-3x+22$. If  $x-2$ is a factor of $p(x)=4x^2-3x+22$, then $p(2)=0$.

Let us plug in $x=2$ in to the function to see if it will give us zero.

$p(2)=4(2)^2-3(2)+22$

We simplify to obtain,

$p(2)=4(4)-3(2)+22$

$p(2)=16-6+22$

$p(2)=10+22$

$p(2)=32$

Since  $p(2)\ne0$, $x-2$ is not a factor of $p(x)=4x^2-3x+22$.