Please help me with algebra 2

Question

What is the remainder when f(x)=x⁴+x³--x²+5x-4 is divided by x+3

Answer 1

The easiest and fastest way is to evaluate f(-3) = (-3)⁴+(-3)³-(-3)²+5(-3)-4

f(-3)=81-27-9-15-4 = 26

See polynomial remainder theorem to show why this works.

Answer 2

If you know synthetic division, then that's the fastest way to solve this problem.

To do so, you're going to set it up like this (the "-3" comes from the "x+3" factor. The other numbers are the coefficients of what you're trying to divide.

-3 | 1 1 -1 5 -4

______________________

Once you work through the division, it should look like this:

-3 | 1 1 -1 5 -4

-3 6_-15 __30__

1 -2 5 -10 26

(all the numbers should be lined up)

The very last number at the bottom of the last column is your remainder. So the remainder is 26.

If you'd like to work through this problem or similar problems in more detail, feel free tor each out to schedule a lesson :)