Answer: -26
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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.