1. Recall: Factoring Quadratic Trinomial where a = 1

2. Factor
m2 + 6m + 8

3. Factor
y2 + 12y + 11

4. n2 – 20n + 51

5. Factor
r2 – 2r - 48

6. Factor
w2 + 3w - 18

7. Factor
x2 + 4x - 12

8. Factor
m2 – 15m - 16

9. Factor
x2 – 4x - 32

10. Factor
26 – 15b + b2

11. Factor
z + z2

12. Factoring Trinomials of the form ax2 + bx + c where a ≠ 1
Topic
Factoring Trinomials of the form ax2 + bx + c where a ≠ 1

13. In factoring trinomials when the coefficient of x2 is not equal to 1
In factoring trinomials when the coefficient of x2 is not equal to 1. We commonly used a trial and error method in factoring a trinomial in the form ax2 + bx + c, this means that we express the polynomials as the product of two binomials. Such trinomials when factored have a general form.

14. ( mx + n ) ( px + q ) = mpx2 + ( mq + np ) x + nq Where: mp = a , the coefficient of x2 and is not equal to 1. mq + np = b, is the coefficient of x nq = c, the third term

15. Examples
Factor 3x2 + 10x + 7
Solution: Factor the first and last terms.
3x x , x
, 1
Write the possible factor combination, we have
( 3x + 7 ) ( x + 1 )
(3x + 1) ( x + 7)
Answer: (3x+7) (x+1)

16. 2. Factor 6x2 – 7x – 10 Solution: Factor the first and last terms
2. Factor 6x2 – 7x – 10 Solution: Factor the first and last terms. 6x2 - 6x , x, 3x, x , 2, -2, 5, -10, 1 Answer: (6x+5) (x-2)

17. Try this!
8y2 + 33y + 4
2a2 – 27a – 14
2x2 – 3x + 1

18. Homework
Factor the following. 1.) 3m2 – 2m – 8 2.) 3a2 – 10a ) 6x2 – x – 2 4.) 4b2 + 12b ) 3x2 – 13x - 10