Remainder Theorem

Remainder Theorem (Question)

Determine the remainder of the function f(x) = 3x² + 5x + 1 when it is divided by the following linear factor.

1. x + 1
2. x – 1
3. 3x – 1

Guide:

When a polynomial, f(x) is divided by a linear factor, (x-a), where a is equal to number. It will results a quotient q(x) with possible a reminder of r(x). The relationship between f(x), linear factor, quotient and the remainder can be written as follow.

• f(x) = Quotient * (1/Linear Factor) + Remainder

Since dividing f(x) by (x-a) will results a remainder of r(x). Thus,

• f(a) = Remainder

If f(a) = 0, then x-a is a factor of the function (factor theorem).

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