Question

Need Help with some Math


Determine the remainder when f(x) = 3x^15 - 5x^12 + 7x^6 - 3x^2 + 12 is divided by x + 1

Answer 1

Answer:

8

Step-by-step explanation:

We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial $f(x)$ being divided by a factor in the form of $(x-a)$, then the remainder of the polynomial is given by $f(a)$.

We have the polynomial:

$f(x)=3x^{15}-5x^{12}+7x^6-3x^2+12$

And it is being divided by:

$(x+1)$

We can rewrite our factor as:

$(x-(-1))$

Therefore:

$a=-1$

Then our remainder will be:

$f(-1)$

Evaluate:

$\begin{aligned} f(-1)&=3(-1)^{15}-5(-1)^{12}+7(-1)^6-3(-1)^2+12\\&=-3-5+7-3+12\\&=8 \end{aligned}$

So, our remainder will be 8.