Question

When a polynomial p(x) is divided by x^2-5, the remainder is x+4. Find the remainder when p(x) + p(-x) is divided by x^2-5?

I am so confused, it would be great if anyone can tell me how to do the question

Answer 1

p(x) = (x^2-5)*q(x) + x+4
p(-x) = (x^2-5)*q(-x) + (-x+4)
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p(x)+p(-x) = (x^2-5)(q(x)+q(-x)) + 8
so the remainder is 8

check: if
p(x) = (x^2-5)(5x^4-2x^3+7x^2+11x-9) + x+4
p(-x) = (x^2-5)(5x^4+2x^3+7x^2-11x-9) - x+4
p(x)+p(-x) = (x^2-5)(10x^4+14x^2-18) + 8

Answer 2

Thanks so much !!!