Factoring Special Products. 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:

Factoring Special Products

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.

Factoring: The reverse of multiplication Use the distributive property to turn the product back into factors. To do this, look for the GCF!

Example: 5x 2 -15x GCF = 5x Pull out 5x from each term! 5x(x-3) is the factored form

12x 2 -18x+6 GCF=6 6(2x 2 -3x+1)

Factoring Special Products a 2 -b 2 =(a+b)(a-b) This is the difference of 2 squares!

Perfect Square Trinomial Pattern *Look to see if the first and last terms are perfect squares, and the middle term is 2ab - if so - it will factor into

FACTOR: Perfect square polynomial: (4y + 3) 2

Difference of perfect squares: (9-3x 2 )(9+3x 2 )

Doesn’t factor, no common factor except 1!

Perfect square polynomial: (2c-9) 2