Factoring Quadratic Trinomials Focus 9 Learning Goal HS
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Factoring Quadratic Trinomials
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- = Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features. APR. B. 3, HS. A-REI. B. 4) 4 3 2 1 0 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.
2 ax +bx+c Remember: To factor trinomials, look at the a, b, c numbers
Steps to Follow: 1. Multiply a*c 2. Set up a t-chart 3. Look for factors of “ac” that added together give you “b” 4. Write answer in (x )
2 x -x-12 1. Multiply ac 2. Set up t-chart (x+3)(x-4) 1(-12)=-12 ac=-12 Sum=-1 b one + one 1(-12) -11 -1(12) 11 -2(6) 4 2(-6) -4 3(-4) -1
Factor 2 x - 1. Multiply ac 2. Set up t-chart (x - 2)(x - 3) 5 x + 6 1(6)=6 ac=6 Sum=-5 two - b -1(-6) -7 -2(-3) -5
Factor when 1 isn’t the number in front of x 2 6 x 2 + 7 x-5 1. Multiply ac 6(-5)=-30 2. Set up ac=-30 t-chart one + one 3. Since you have a coefficient greater than 1, take your factored terms and factor them too. (2 x - 1)(3 x + 5) -1(30) 1(-30) -2(15) 2(-15) -3(10) Sum=7 b 29 -29 13 -13 7
