Sec-32 - Math 1300 Operations with Polynomials Section 3.2...

Math 1300 Section 3.2 Notes
1
Operations with Polynomials
Addition of Polynomials
The sum of two polynomials is found by combining like terms. To add like terms, add the
coefficients and do not change the variable and exponents in common.
Example: Perform the addition (2 x
7
+ 9 x
3
- 5) + (3 x
3
+ 2 x + 14).
(2 x
7
+ 9 x
3
- 5) + (3 x
3
+ 2 x + 14)
Remove the parentheses and group like terms together
2 x
7
+ 9 x
3
+ 3 x
3
+ 2 x + 14 - 5
Combine like terms. Don’t change variables or exponents.
2 x
7
+ 12 x
3
+ 2 x + 9
Answer.
Example: Perform the addition (2 x
3
- 17 x
2
- 5x) + (3 x
3
- x + 8).
(2 x
3
- 17 x
2
- 5x) + (3 x
3
- x + 8)
Remove the parentheses and group like terms together
2 x
3
+ 3 x
3
- 17 x
2
- 5x - x + 8
Combine like terms. Don’t change variables or exponents.
5 x
3
- 17 x
2
- 6x + 8
Answer.
Subtraction of Polynomials
The difference of two polynomials is found by adding the first polynomial to the negative of the
second polynomial. The negative of the second polynomial is found by changing the sign of
each term of the polynomial.
Example: Perform the subtraction (9 x
5
+ 2 x
3
- 1) - (2 x
3
+ 4 x - 4).
(9 x
5