Question

if p(x) leaves a remainder a and -a when divided by x+a and x-a, the remainder when p(x) is divided by x^2-a^2 is ??
Please give detailed answer!

Answer 1

Answer:

p(x)=(x-a)q(x)+r(x)

where q(x) is the quotient when f(x) is divided by x-a and r(x)

The Remainder Theorem says that we can restate the polynomial in terms of the divisor, and then evaluate the polynomial

x=a

hence putting it we get

p(a)=0*q(a)+r(a)

p(a)=r(a)

hence the remainder is p(a)