The Remainder Theorem The Remainder Theorem says that : If a polynomial f(x) is divided by a linear divisor x – a, the remainder is f(a) So for example when 4x3 - 5x + 1 is divided by x - 2 the remainder will be f(2) or remainder = 4(2)3 - 5(2) + 1 = 32 - 10 + 1 = 23 Note : We had to fill in with a 2 not a -2, because Therem says the divisor must be x - a When 4x3 - 5x + 1 is divided by x + 3 the remainder will be f(-3) or remainder = 4(-3)3 - 5(-3) + 1 = -98 + 15 + 1 = -92 So we can use the Remainder Theorem or we can use synthetic division to get the remainder of polynomial division when the divisor is of degree 1. If the remainder is 0 then the divisor is a factor of the dividend.