factor theorem notes

REMAINDER & FACTOR
THEOREMS
THE REMAINER THEOREM

• If a function is divided by , the remainder is

• If a function is divided by , the remainder is
• If a function is divided by , the remainder is




THE FACTOR THEOREM



EXERCISE 1: (Remainder & Factor theorems)

• For each of the following, determine the remainder if

• is divided by
• is divided by
• is divided by
• is divided by

• Given:

• Use the remainder theorem and determine the remainder if is divided
by
•
•
• What may be concluded from the previous two calculations?

• Prove that is a factor of .

• Given:
Determine the value of p if is a factor of .

• Given:

• If is a factor of , show that .
• Hence, determine the values of a and b if it is further given that
the remainder is 48 when is divided by .