1. Factoring Quadratic Trinomials

2. 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.

3. ax 2 +bx+c Remember: To factor trinomials, look at the a,b,c numbers

4. 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 )(x )

5. x 2 -x-12 1. Multiply ac 1(-12)=-12 2. Set up t-chart ac=-12 one + one - Sum=-1 1(-12) -1(12) -2(6) 2(-6) 3(-4) -11 11 4 -4 (x+3)(x-4) b

6. Factor x 2 - 5x + 6 1. Multiply ac 1(6)=6 2. Set up t-chart ac=6 two - Sum=-5 -1(-6) -2(-3) -7 -5 (x - 2)(x - 3) b

7. Factor when 1 isn’t the number in front of x 2 6x 2 + 7x-5 1. Multiply ac 6(-5)=-30 2. Set up t-chart 3. Since you have a coefficient greater than 1, take your factored terms and factor them too. ac=-30 one + one - Sum=7 -1(30) 1(-30) -2(15) 2(-15) -3(10) 29 -29 13 -13 7 (2x - 1)(3x + 5) b