Multiplying Polynomials. 43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math.

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Presentation transcript:

Multiplying Polynomials

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features. - Factor using methods including common factors, grouping, difference of two squares, sum and difference of two cubes, and combination of methods. - Add, subtract, and multiply polynomials, - Explain how the multiplicity of the zeros provides clues as to how the graph will behave. - Sketch a rough graph using the zeros and other easily identifiable points. Students will factor polynomials using limited methods, perform operations (excluding division) on polynomials, and identify key features on a graph. - Add and subtract polynomials. - Multiply polynomials using an area model. - Factor polynomials using an area model. - Identify the zeros when suitable factorizations are available. - Identify key features of a graph. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 9 Learning Goal – (HS.A-SSE.A.1, HS.A-SSE.A.2, HS.A-SEE.B., HS.A- APR.A.1, HS.A-APR.B.3, HS.A-REI.B.4) = Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features.

1. 5x(3x 2 -2x+1) (give the 5x to each term) 5x(3x 2 )+5x(-2x)+5x(1) 15x 3 -10x 2 +5x 2. 6x 2 (5x 2 +3x-9) 30x 4 +18x 3 -54x 2 Simple multiplication: Distribute monomial to all terms!

FOIL Ffirst terms Oouter terms Iinner terms Llast terms

(2x-3) (3x+4) = 2x  3x + 2x  4 + (-3)  3x + (-3)  4 =6x 2 + 8x - 9x - 12 =6x 2 -x-12 Practice: (5x+3) (4x-6) 20x 2 – 30x + 12x – 18 20x 2 – 18x - 18

Distributive Property (x-2)(5+3x-x 2 ) =x(5+3x-x 2 )+(-2)(5+3x-x 2 ) = 5x + 3x 2 - x 3 – x + 2x 2 =-x + 5x 2 - x (put in order) =-x 3 +5x 2 -x-10

Special Products: Square of a binomial (a+b) 2 = a 2 +ab+ab+b 2 = a 2 +2ab+b 2 (a-b) 2 =a 2 -ab-ab+b 2 =a 2 -2ab+b 2

RULE: You can do this mentally when you recognize the pattern! (x+2) 2 (x-6) 2 x 2 + 2x + 2x + 4 x 2 +4x+4 x 2 -12x+36

Product of the sum and difference of two terms: (a+b) (a-b)=a 2 +ab-ab-b 2 =a 2 -b 2 The middle terms cancel out and you end up with the difference of perfect squares. (5x+2) (5x-2)= 25x 2 -4

PRACTICE : (x+2) (x-2) (b+6) 2 (y-4) 2 x b b + 36 y 2 - 8y + 16