remainder theorem

REMAINDER THEOREM: The remainder of the division of a polynomial, P(x), by (x – a) equals the value of the polynomial when x = a, P(a).

Proof:

Example: The remainder if we divide P(x)= x³ -3x +7 by (x – 3) equals P(3)= 3³ - 3·3 + 7 = 25

Exercise: calculate the remainder when we divide x⁴ - x² + 1 by:

a) x - 2

b) x + 3

c) x - 3

Solutions: a) 13; b) 73; c) 73