1. Adding and Subtracting Polynomials
3.4
Adding and Subtracting Polynomials

2. Adding and Subtracting Polynomials
To Add Polynomials
Combine all the like terms.
To Subtract Polynomials
Change the signs of the terms of the polynomial being subtracted, and then combine all the like terms.

3. Adding and Subtracting Polynomials
Example
Add: (3x – 8) + (4x2 – 3x +3)
(3x – 8) + (4x2 – 3x +3)
= 3x – 8 + 4x2 – 3x + 3
= 4x2 + 3x – 3x – 8 + 3
= 4x2 – 5

4. Adding and Subtracting Polynomials
Example
Subtract.
1) 4 – (– y – 4)
= 4 + y + 4
4 – (– y – 4)
= y
= y + 8
2) (– a2 + 1) – (a2 – 3) + (5a2 – 6a + 7)
(– a2 + 1) – (a2 – 3) + (5a2 – 6a + 7)
= – a2 + 1 – a a2 – 6a + 7
= – a2 – a2 + 5a2 – 6a
= 3a2 – 6a + 11

5. Helpful Hint
Don’t forget to change the sign of each term in the polynomial being subtracted.

6. Adding and Subtracting Polynomials
You can also use a vertical format in arranging your problem, so that like terms are aligned with each other vertically.