Factoring!! Need help!! FOIL not allowed. Question is 4x^2+38x +70. Full question in description!

Question

Ok so I’m factoring, by using the x method and box method. I’m not allowed to use FOIL. The question is 4x^2+38x+70. So far I’ve found the GCF, which is 2. I’m not sure about the rule regarding multiplying A and C (4 and 70 in this problem), but I also heard my teacher say something about dividing by the GCF and I’m not sure which to do first???

Answer 1

4x² + 38x + 70

2(2x² + 19x + 35)

Now 2 * 35 = 70

70 = 2 * 5 * 7

19 = 2 * 7 + 5

2(2x² + 5)(x + 7)

Answer 2

4x^2+38x+70

divide by 2

2(2x^2+19x+35)

multiply 2*35=2*5*7

group the factors such that the factors sum to 19

2*5*7=5*(2*7)=5*14 and 5+14=19

factor

2x^2+19x+35

(2x+5)(x+7)

now put the 2 back in

2(2x+5)(x+7) answer