Adding and Subtracting Polynomials (9.1)

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Presentation transcript:

Adding and Subtracting Polynomials (9.1) Objective: Students will add and subtract 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

b) (-3x3 + 11x2 – 8x + x5 + 2) + (8x – 2x4 + 7x3 – 3 + 12x2) #2 Add Polynomials a) (2x2 + x – 5) + (x + x2 + 6 ) 2x2 + x – 5 x2 + x + 6 3x2 + 2x + 1 b) (-3x3 + 11x2 – 8x + x5 + 2) + (8x – 2x4 + 7x3 – 3 + 12x2) x5 + 0x4 – 3x3 + 11x2 – 8x + 2 0x5 – 2x4 + 7x3 + 12x2 + 8x – 3 x5 – 2x4 + 4x3 + 23x2 – 1

Check Point: c) (2x6 – x5 + 3x3 – 14x2 +13) + (7x5 – x4 + 9x3 + 13x2+ 2) 2x6 – x5 + 0x4 + 3x3 – 14x2 + 0x + 13 0x6 + 7x5 – x4 + 9x3 + 13x2 + 0x + 2 2x6 + 6x5 – x4 + 12x3 – x2 + 15 2x6 + 6x5 – x4 + 12x3 – x2 + 15

(-3x3 + 11x2 – 8x + x5 + 2) – (2x – 4x4 – 3x3 – 3 + 6x2) #3 Subtract Polynomials (11x4 + x3 – x + 5) – (-x4 – x2 + 2x + 8 ) 11x4 + x3 + 0x2 – x + 5 +x4 + 0x3 + x2 – 2x – 8 12x4 + x3 + x2 – 3x – 3 (-3x3 + 11x2 – 8x + x5 + 2) – (2x – 4x4 – 3x3 – 3 + 6x2) x5 + 0x4 – 3x3 + 11x2 – 8x + 2 0x5 + 4x4 + 3x3 – 6x2 – 2x + 3 x5 + 4x4 + 5x2 – 10x2 + 5

Check Point: (3x5 + 7x3 – 13x2 – 10x + 9) – (x5 – 4x4 + 11x2 – 2x – 7 ) 3x5 + 0x4 + 7x3 – 13x2 – 10x + 9 -x5 + 4x4 + 0x3 – 11x2 + 2x + 7 2x5 + 4x4 + 7x3 – 24x2 – 8x + 16 2x5 + 4x4 + 7x3 – 24x2 – 8x + 16

A B C Find the length of in terms of x. 1) + = 2) =

Find the area of quadrilateral ABCD in terms of x. A B + C D

A B C Find the length of in terms of x. 1) = 2) =

Find the area of if the area of rectangle LMNO is . L M P O N

Assignment Book Pg. 373 # 1 – 8 all # 15 – 20 all # 23, 24, 28, 36, 37, 45, 61, 66, 70