1. Objective The student will be able to: factor trinomials of the type ax 2 + bx + c with grouping. Designed by Skip Tyler, Varina High School

2. 1) Factor y 2 + 7y + 12 +12 +7 The goal is to find two factors in the first column that add up to the middle term in the second column. Replace the middle number of the trinomial with our working numbers from the table y 2 + 7y + 12 y 2 + 3y + 4y + 8 +1, +12 +2, +6 +3, +4 +13, NO +8, NO +7, YES!!

3. 1) We have two groups! y 2 + 3y + 4y + 8 Find the GCF of each group and factor it out. y(y + 3) +4(y + 3) (y + 4)(y + 3) You can check it by multiplying. If things are done right, the parentheses should be the same. Factor out the GCF’s. Write them in their own group.

4. 2) Factor 6n 2 + 23n + 7 Create your table. 1, 42 2, 21 6, 7 MultiplyAdd 42 23 Product of the first and last coefficients Middle coefficient 43 23 13 Signs need to be different since number is negative. M A

5. Replace the middle term with our working numbers. 6n 2 + 23n + 7 6n 2 + 2n + 21n + 7 Group the terms. 6n 2 + 2n + 21n + 7 Factor out the GCF 2n(3n + 1) +7(3n + 1) The parentheses are the same! (2n + 7)(3n +1)

6. 3) Factor 7x 2 – 26x – 8 Create your table. MultiplyAdd -56 -26 Product of the first and last coefficients Middle coefficient -56, 1 -1, 56 -2, 28 -28, 2 -4, 14 -14, 4 -55 55 26 -26 10 -10 Signs need to be different since number is negative. M A

7. Replace the middle term with our working numbers. 7x 2 – 26x – 8 7x 2 – 28x + 2x – 8 Group the terms. 7x 2 – 28x + 2x – 8 Factor out the GCF 7x(x – 4) +2(x – 4) The parentheses are the same! (7x + 2)(x – 4)

8. 4) Factor 5x 2 - 17x + 14 Create your table. MultiplyAdd +70 -17 Product of the first and last coefficients Middle coefficient -1, -70 -2, -35 -7, -10 -71 -37 -17 Signs need to be the same as the middle sign since the product is positive. Replace the middle term. 5x 2 – 7x – 10x + 14 Group the terms. M A

9. 5x 2 – 7x – 10x + 14 Factor out the GCF x(5x – 7) -2(5x – 7) The parentheses are the same! (x – 2)(5x – 7) Replace the middle term. 5x 2 – 7x – 10x + 14 Group the terms.

10. Factor 2x 2 + 9x + 10 1.(2x + 10)(x + 1) 2.(2x + 5)(x + 2) 3.(2x + 2)(x + 5) 4.(2x + 1)(x + 10)

11. Factor 6y 2 – 13y – 5 1.(6y 2 – 15y)(+2y – 5) 2.(2y – 1)(3y – 5) 3.(2y + 1)(3y – 5) 4.(2y – 5)(3y + 1)