HELP ASAP. THIS IS DUE TONIGHT! What is the remainder when the polynomial p(x)= 5x^3 + x^2 + 10 is divided by (x + 2)?

Remainder theorem:

If you divide p(x) by (x-k), then the remainder is r = p(k)

Comparing x+2 to the form x-k, we see that k = -2

It might help to rewrite x+2 as x - (-2) to match the forms better.

Now plug this into the p(x) function getting...

p(x) = 5x^3 + x^2 + 10

p(k) = 5k^3 + k^2 + 10

p(-2) = 5(-2)^3 + (-2)^2 + 10

p(-2) = 5(-8) + 4 + 10

p(-2) = -40 + 4 + 10

p(-2) = -36+10

p(-2) = -26

The remainder is -26

You can use polynomial long division or synthetic division to confirm this.