1. Polynomial Functions and Adding and Subtracting Polynomials
5.2
Polynomial Functions and Adding and Subtracting Polynomials

2. Polynomial Vocabulary
Term – a number or a product of a number and variables raised to powers
Coefficient – numerical factor of a term
Constant – term which is only a number
Polynomial is a sum of terms involving variables raised to a whole number exponent, with no variables appearing in any denominator.

3. Polynomial Vocabulary
In the polynomial 7x5 + x2y2 – 4xy + 7,
there are ____terms:
The coefficient of term 7x5 is ____,
of term x2y2 is ____,
of term – 4xy is ____ and
of term 7 is ____.
_____ is a constant term.

4. Types of Polynomials Monomial is a polynomial with one term.
Binomial is a polynomial with two terms.
Trinomial is a polynomial with three terms.

5. Degrees Degree of a term
To find the degree, take the _______ of the exponents on the variables contained in the term.
Degree of a constant is _____.
Degree of the term 5a4b3c is ____ (remember that c can be written as c1).
Degree of a polynomial
To find the degree, take the largest degree of any term of the polynomial.
Degree of 9x3 – 4x2 + 7 is 3.

6. Example
If P(x) = 3x2 – 2x – 5, find the following,
a. P(1)
b. P(–2)

7. Combining Like Terms Example:
______________are terms that contain exactly the same variables raised to exactly the same powers.
Warning!
Only like terms can be combined through addition and subtraction.
Example:
Combine like terms to simplify.
x2y + xy – y + 10x2y – 2y + xy

8. Adding Polynomials Adding Polynomials
To add polynomials, combine all the like terms.
Example:
Add.
(3x – 8) + (4x2 – 3x +3)

9. Subtracting Polynomials
To subtract two polynomials, change the signs of the terms of the polynomial being subtracted and then add.
Example:
a) Subtract
4 – (– y – 4)
b) Simplify (– a2 + 1) – (a2 – 3) + (5a2 – 6a + 7)