Recall Factoring Quadratic Trinomial where a 1 Factor

Recall: Factoring Quadratic Trinomial where a = 1

Factor 2 m + 6 m + 8

Factor 2 y + 12 y + 11

2 n – 20 n + 51

Factor 2 r – 2 r - 48

Factor 2 w + 3 w - 18

Factor 2 x + 4 x - 12

Factor 2 m – 15 m - 16

Factor 2 x – 4 x - 32

Factor 26 – 15 b + 2 b

Factor 48 + 19 z + 2 z

Topic Factoring Trinomials of the 2 form ax + bx + c where a ≠ 1

In factoring trinomials when the coefficient of x 2 is not equal to 1. We commonly used a trial and error method in factoring a trinomial in the form ax 2 + bx + c, this means that we express the polynomials as the product of two binomials. Such trinomials when factored have a general form.

( mx + n ) ( px + q ) = mpx 2 + ( mq + np ) x + nq Where: mp = a , the coefficient of x 2 and is not equal to 1. mq + np = b, is the coefficient of x nq = c, the third term

Examples 1. Factor 3 x 2 + 10 x + 7 Solution: Factor the first and last terms. 3 x 2 3 x , x 7 7 , 1 Write the possible factor combination, we have ( 3 x + 7 ) ( x + 1 ) (3 x + 1) ( x + 7) Answer: (3 x+7) (x+1)

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

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

Homework Factor the following. 1. ) 3 m 2 – 2 m – 8 2. ) 3 a 2 – 10 a + 8 3. ) 6 x 2 – x – 2 4. ) 4 b 2 + 12 b + 9 2 5. ) 3 x – 13 x - 10