Factor trinomials by grouping?

Question

How do you factor these two separate equations?:

6x²+x-57

And also...

2x²-2x-12

Answer 1

grouping is only effective with four expressions, for these you would use the Quadratic equation or the simpler method. first fine factors of the a and c values. So for 6 the factors are 1,2,3,6 and 57 is 1,3,19,57. then you multiply the factors so that the result would give a sum equal to the b value which is 1.

so for 6 use: 6 and 1. and for 57 use -3 and 19. 6*-3=18. 1*19 = 19. 19+(-18)=1. so the factor is (6x+19)(x-3).

the second equation you should factor out 2, because it's the highest common factor for each expression so

(2x^2 - 2x - 12)/2 =x^2 -x -6. then you do the factoring like in the first problem. for 1 factor is 1 and for 6 factors are 1,2,3,6. the sum should be equal to -1. so its 1*-3=-3 and 1*2=2. factor should be (x+2)(x-3)