Question

A polynomial p(x), when divides by x-a gives the remainder p(a). Which of the these can be the degree of the polynomial p(x)
1- any whole number
2- any integer
3- any rational number
4- any natural number

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)