5.1 M ONOMIALS 5.2 POLYNOMIALS 7.7 O PERATIONS WITH FUNCTIONS Algebra II w/ trig.

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5.1 M ONOMIALS 5.2 POLYNOMIALS 7.7 O PERATIONS WITH FUNCTIONS Algebra II w/ trig

5.1 M ONOMIALS A. Properties of Exponents: Let a and b be nonzero real numbers. Let m and n be integers. Product of Powers: Quotient of Powers: Power of a Power: Power of a Product: Power of a Quotient: Negative Powers:

B. Examples: Simplify. Assume that no variable equals

5.6.

7.8.

9.

5.2 P OLYNOMIALS A. Definitions: Terms Definitions Examples MonomialA constant, variable, or product of a constant and one or more variables. -7, x, -2st, s 2 t 4 ConstantA number.-2, ½, 0 CoefficientThe constant (or numerical) factor in a monomial. 3m 3, -st, u Degree of a Monomial The sum of the degrees of the variables. *a constant has a degree of ZERO. 6xy 3, -s 2 t 3, -8 PolynomialA monomial or sum of monomials.x 2 – 4x + 5, 3 (x + 1) Degree of a Polynomial The greatest of the degrees of its terms after it has been simplified. x 4 – 2x 2 y 3 + 6y – 11

I. Polynomial or Not? State the degree if possible. A.B. C.D. E.

II. To add or subtract polynomials --perform the indicated operations and combine like terms A. B.

III. Multiply by using the distributive property. A. B.

IV. Multiplying Binomials by using the FOIL Method: A. B. C.

7.7 Operations on Functions Sum: Difference: Product: Quotient:

Find the sum, difference, and product. 1.

2.