Download Section 12.4

Saturday, March 8, 2008
Section 12.4 (Addition and Subtraction of Polynomials)

To add two polynomials, you can just write a plus sign between them and collect like terms
Examples:
(-4x3 +
1 2
x + 2x – 3) + (8x3 – 2x2 + 8) =
2
(3 – 3x2 + 13x4) + (1 + x + 3x2 + x3) = (note order)

You can also add polynomials by writing them in columns
Example: (11x2 – x + 4) + (-2x2 – 3) =>


To find the opposite / additive inverse of a number, we can multiply that same number by negative 1,
resulting in changing the sign (opposite of 1 is -1, opposite of -3.2 is 3.2)
The same is true with polynomials
Examples: Simplify
-(7n4 – 5n2 + 4) =

-(-
1 5
5
x + 2x3 - x) =
3
2
Subtracting polynomials is equivalent to adding their opposites (just as in real numbers)
Examples:
(9x5 + 3x3 – 2x + 4) – (7x5 – 11x4 + 3x3 + 1) =
(3n2 + 3n + 3) – (-n2 + 2n + 2) =
(17x3 + 3x2 – 3) – (x2 – 3) = (use columns)
Example: Find a polynomial for the sum of the perimeters and areas of the following rectangles
½x
2x
x
x
2x
x
Additional Homework from Book: 4, 7, 11, 18, 25, 29, 35, 37, 39, 42