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!
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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!
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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)