Notes On Polynomials

Adding Polynomials

To add polynomials you combine the like terms.
Example:
$(2x^2+3x+4) + (x^2-2x-5)$

Simplifies to
$3x^2 + x -1$

Subtracting Polynomials

To subtract polynomials you add the opposite of each term.
Example
$(2x^2+3x+4) - (x^2 + 2x-5)$

Simplifies to
$2x^2 + 3x +4 -x^2 - 2x + 5$

and then further to
$x^2 + x + 9$

Multiplying Polynomials

To multiply polynomials you have to do four different multiplications
F - First Pair
O - Outside Pair
I - Inside Pair
L - Last Pair

Example:
$(2x + 3)(4x - 1)$
First: $(2x)(4x) = 8x^2$
Outside: $(2x)(-1) = -2x$
Inside: $(3)(4x) = 12x$
Last: $(3)(-1) = -3$

Now add your results together:
$8x^2 - 2x + 12x -3$
and combine any like terms
$8x^2 + 10x -3$