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Remainder Theorem

Question

What is the remainder of the function f(x) = 2×2 + 2x + 5 when it is divided by the following linear factor?

  1. x – 1
  2. x + 1
  3. 1 – 3x

Answer

  1. 9
  2. 5
  3. 53/9

Note:

When a polynomial, g(x) is divided by a linear factor, (x-b), where b 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.

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

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

g(b) = Remainder

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

 

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