Multiplying Polynomials Objective: Students will multiply polynomials.

Algebra Standards: 10.0 Students add, subtract, multiply and divide monomials and polynomials. Students solve multi-step problems, including word problems, using these techniques.

is a number, a variable, or the product of a number and one or more Vocabulary Monomial is a number, a variable, or the product of a number and one or more variables with whole number exponents. 8 -2x -3x2y ½x2 Degree of a Monomial is the sum of the exponents of the variables in the monomial. -2x -3x2y 5 -3x5 1 3 5

Vocabulary Polynomial is a monomial or a sum of monomials 4x3 -2x + 2 7x2 – 4x + 6 Binomial: two-term polynomial x + 2 4x3 + 2x -2x2 – 5 Trinomial: three-term polynomial x2 + 2x – 1 5x5 – 5x + 2 -x4 + 2x2 – 4x

Polynomial Degree Identified by Degree Identified by Number of Terms #1 Identify Polynomials Polynomial Degree Identified by Degree Identified by Number of Terms a) -3 constant monomial 1 linear binomial b) –x + 1 2 quadratic binomial c) x2 + 3 d) 5x3 – 3x2 + x – 8 3 cubic polynomial

a) 4(x +3) = 4x + 12 b) -4a(a +3) = -4a2 – 12a c) 4b(2b2 + 3b – 2) = #1 Distributive Property a) 4(x +3) = 4x + 12 b) -4a(a +3) = -4a2 – 12a c) 4b(2b2 + 3b – 2) = 8b3 + 12b2 – 8b

a) (x + 3) (x – 2) First Outer Inner Last x2 -2x +3x -6 x2 + x – 6 #2 Use FOIL a) (x + 3) (x – 2) First Outer Inner Last x2 -2x +3x -6 x2 + x – 6 b) (3x – 2) (x + 2) First Outer Inner Last 3x2 +6x -2x -4 3x2 + 4x – 4

(5x – 4) (3x – 6) First Outer Inner Last 15x2 -30x -12x +24 15x2 – 42x Check Point: (5x – 4) (3x – 6) First Outer Inner Last 15x2 -30x -12x +24 15x2 – 42x + 24 d) (2x + 3)(x + 10) First Outer Inner Last 2x2 +20x +3x +30 2x2 + 23x + 30

(4 – x)(8 – 11x + x2) = 32 – 44x + 4x2 – 8x + 11x2 – x3 = – x3 + 15x2 #3 Distributive Property – more than two terms (4 – x)(8 – 11x + x2) = 32 – 44x + 4x2 – 8x + 11x2 – x3 = – x3 + 15x2 – 52x + 32 b) (x + 2)(x2 – 3x + 5) = x3 – 3x2 + 5x + 2x2 – 6x + 10 = x3 – x2 – x + 10

Assignment Book Pg. 531 # 3-11, 21-37 odds ( use FOIL or Box )