When polynomials are multiplied, each term of one expression is
multiplied by every term of the other expression. Then the terms in
the product are added.
Choose one polynomial, preferably the longest, and then:
- multiply it by the first term of the other polynomial
- then multiply it by the second term of the other polynomial
then multiply it by the third term of the other polynomial (if any)
- lastly, add up the products.
Multiply the following polynomials:
We first multiply our first polynomial by the first term of the
second polynomial then we multiply it by the second term of the
Lastly we simplify and add up the products
When we are dividing a polynomial by something more complicated
than just a simple monomial, then we will need to use a different
method for the simplification. This method is called "long
(polynomial) division", and it works just like the long (numerical)
division you did back in elementary school, except that now you're
dividing with variables.
We will show the procedure in an example.
Divide x2-2x-8 by x+2:
First, we set up the division, writing x+2 to the left and
x2-2x-8 to the right. Our result comes out on top of the
polynomials. In order to see exactly how this is done watch our
video lesson below.
Videolesson: Divide x2-2x-8 by x+2
(same as the example above).