Download Vocabulary: Adding Polynomials: Subtracting Polynomials

ALGEBRA 2
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Vocabulary:

Polynomial:
o An expression of more than two algebraic terms, especially the sum of several terms that contain
different powers of the same variable(s)
 Example: 3𝑥 4 + 2𝑥 3 − 9𝑥 2 + 7𝑥 − 5

Term:
o A single number or variable, or numbers and variables multiplied together
o Terms are separated by + or − signs
Adding Polynomials:


To add polynomials, add the coefficients of the like terms.
DO NOT CHANGE THE EXPONENTS!!!
Examples:
1) (4𝑥 2 + 5𝑥 − 1) + (2𝑥 2 − 2𝑥 + 5) =
2) (3𝑥 3 − 𝑥 − 4) + (2𝑥 3 + 2𝑥 2 − 5𝑥 − 2) =
Subtracting Polynomials:


To subtract polynomials, add the opposite of each term of the polynomial being subtracted.
o Distribute the subtraction through to every term in the second polynomial to change the signs, then add.
DO NOT CHANGE THE EXPONENTS!!!
Examples:
3) (4𝑥 2 − 4𝑥 − 4) − (2𝑥 2 − 5𝑥 + 2) =
4) (3𝑥 3 − 9𝑥 2 + 6𝑥 − 3) − (−2𝑥 3 − 8𝑥 2 + 2𝑥 − 3) =
Distributive Property with Polynomials:


First, multiply in the value in front of the parentheses
o Use exponent rules: add exponents
Then, add like terms
o DO NOT CHANGE EXPONENTS
5) 𝑥(𝑥 2 + 4𝑥 − 3) + 2𝑥(3𝑥 − 4) =
6) −2𝑥 2 (3𝑥 3 − 𝑥 + 6) − 4𝑥(2𝑥 4 + 2𝑥 3 − 4𝑥 2 − 4) =
Practice from Textbook:
To multiply polynomials, use the FOIL technique:
F.
O.
I.
L.
Examples:
7) (𝑥 − 3)(𝑥 + 4)
8) (2𝑥 + 5)(𝑥 + 3)
9) (𝑥 − 5)(𝑥 + 5)
10) (𝑥 + 8)(𝑥 + 8)
11) (5𝑥 2 − 2𝑥 + 5)(𝑥 − 1)
12) (3𝑥 − 4)2