1. Combine any like terms and write the resulting polynomial in descending order.
1) x – x2 + x
= 5x x – 3
2) 3x + 2x – 6x x – 7
= – 4x x
Classify and find the degree of each polynomial.
3) 4x – 8
– Binomial
– Degree = 1
4) x x – 6
– Trinomial
– Degree = 2

2. 13.03 Adding and Subtracting Polynomials

3. Polynomials can be added or subtracted using one of two forms: horizontally or vertically.
( 3x2 + 4x + 2 ) + ( 5x2 – 6x + 7 ) or
( 3x2 + 4x + 2 )
+ ( 5x2 – 6x + 7 )
The parentheses have to be removed using the Distributive Property: a( b + c ) = ab + ac.
To do this place a 1 in front of the parentheses. Once the parentheses are removed, combine like terms and write the polynomial in descending order.

4. Add the following polynomials.
( 2x x ) + ( 5x2 – 8x )
1 ( 2x x ) ( 5x2 – 8x )
2x x x2 – 8x + 8
7x2 – 5x + 9
( x x )
+ ( 3x x – 8 )
1 ( x x )
+ 1 ( 3x x – 8 ) =
x x + 6
+ 3x x – 8 =
_______________
4x x – 2

5. Subtract the following polynomials.
( 9x x ) – ( 4x2 – 5x )
1 ( 9x x ) – 1 ( 4x2 – 5x )
9x x – 4x x – 7
5x x – 4
( 6x x )
– ( 2x2 – 4x – 1 )
1 ( 6x x )
– 1 ( 2x2 – 4x – 1 ) =
6x x + 9
– 2x x + 1 =
_______________
4x x

6. Try This:
Add:
( x2 – 2x ) + ( 2x2 – 7x )
1 ( x2 – 2x ) ( 2x2 – 7x )
x2 – 2x x2 – 7x + 1
3x2 – 9x + 7
Subtract:
( 3x2 – 2x ) – ( 5x2 – 8x )
1 ( 3x2 – 2x ) – 1 ( 5x2 – 8x )
3x2 – 2x – 5x x – 2
– 2x x + 4