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Polynomial | Remainder Theorem | Factor Theorem 1/3

A. REMAINDER THEOREM

If f(x) is divided by (x  a) ⇒ the remainder is f(a)

Equate (x-a) to zero all the time

x-a = 0 –> x=a –> substitute “a” into x

Some of you may be irritated by the f and (x) and a, here’s a easier way to understand … go straight to the Polynomial Questions

Remainder Theorem Question:

Find the remainder when 5x3 – 5x + 1 is divided by:
i. x-2, ii. x+3, iii. 2x-1

Ans: Let f(x) = 4x3 – 5x + 1

f(2) = 5(2)3-5(2)+1 = 31 = Remainder

f(-3) = 5(-3)3-5(-3)+1 = -119 = Remainder

it’s divided by x + 3 so since x+3=0 –> x=-3 –> substitute “-3” into x

f(½) = 5(½)3-5(½)+1 = -0.875

it’s divided by (2x-1) so since 2x-1 = 0 –> x=1/2 –>
substitute “1/2” into x

 DON’T waste time doing long division in remainder theorem questions!!!

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