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ALGEBRA 2 Name:_________________________________ Date:_____________ 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