How do I use the remainder theorem to divide #2x^2-5x-1# by #x-3#?

1 Answer
Oct 9, 2014

The remainder theorem results in the output value of the given polynomial after evaluating it at a specific value of #x#.

First you solve the divisor by setting it equal to zero.

#x-3=0#
#x=3#

This #3# will be used to multiply each coefficient of the of the polynomial.

The coefficients of #f(x)=2x^2-5x-1# are #2, -5, and -1#.

We begin by multiplying the value of #x#, which is #3#, by the first coefficient.

This product is then added to the next coefficient. The result of the previous operation is then multiplied by #3# and we continue until we reach last coefficient by repeating the steps above.

The numbers in parentheses are are the coefficients.

#3*(2)=6#

#(-5)+6=1#

#3*(1)=3#

#(-1)+3=2#

By using the remainder theorem we see that #f(3)=2#

Please see the video below for another example.

Remainder Theorem Example