Factoring Quadratics using X-Box method and Factor by Grouping

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Presentation transcript:

Factoring Quadratics using X-Box method and Factor by Grouping

Bell Ringer:

Homework! Score out of 26 Divide by 2.6

X- Marks the Spot Product a∙c factors factors Sum b

Solve using factoring by grouping Example: Factor 3x2 -13x -10 -13x= -15x +2x 1. Plug and solve values of our “X” 2. Substitute new factors in for bx 3x2 -15x+2x -10 (3)(-10)= -30 3. Solve by grouping!  (3x2-15x)+(2x-10) =3x(x-5)+2(x-5) =(x-5)(3x+2) -15 2 -13 4. Check answer: (x-5)(3x+2) 3x2 -13x -10=(x-5)(3x+2)

Solve the x-box way Example: Factor 3x2 -13x -10 x -5 (3)(-10)= -30 3x -15 2 -13 +2 2x -10 3x2 -13x -10 (x-5)(3x+2)

First and Last Coefficients FACTOR the x-box way ax2 + bx + c GCF GCF Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum GCF

Examples Factor using the x-box method. 1. x2 + 4x – 12 x +6 x -12 4 x 6x 6 -2 -2 -2x -12 Solution: x2 + 4x – 12 (x + 6)(x - 2)

Examples 2. x2 - 9x + 20 Solution: x2 - 9x + 20 (x - 4)(x - 5) 20 -4 -5 20 -9 Solution: x2 - 9x + 20 (x - 4)(x - 5)

Examples 3. 2x2 - 5x – 7 2x -7 x Solution: 2x2 - 5x – 7 -7 2 -14 -5 x -7x 2x² +1 2x -7 Solution: 2x2 - 5x – 7 (2x - 7)(x + 1)

Examples 4. 15x2 + 7x – 2 3x +2 5x Solution: 15x2 + 7x – 2 -30 7 5x 15x² 10x 10 -3 -1 -3x -2 Solution: 15x2 + 7x – 2 (3x + 2)(5x - 1)

You Try 2x2 +3x –9 6x2 + x – 2 4x2 + 9x + 2

Partner Activity! On the front side of your Factoring Practice are your questions. On the back side is the answer key for your partner. Work on your own Factoring Practice worksheet and when you want to check your answer, do so with your partner. Remember the purpose of this activity is to help each other to be able to solve the problems. Be good teachers! (Do not just give them the answers) Work on for the time given and get as far as you can!