Factor the following terms: 12x^2+26x+10

Question

Factor the following terms: 12x^2+26x+10

Answer 1

Hi Melissa;

12x²+26x+10

 

For the FOIL, the following are our choices...

FIRST...(6x)(2x) or (4x)(3x) or (12x)(x)

LAST...(10)(1) or (1)(10) or (5)(2) or (2)(5)

 

As to the FIRST, the larger number must come first.  Therefore, (2x)(6x) is not an option, etc.

 

The (6x)(2x) combination is compatible with the (10)(1) combination to produce 26x because (6)(1)=6 and (10)(2)=20...6+20=26.

 

(6x+10)(2x+1)

Let's FOIL...

FIRST...(6x)(2x)=12x²

OUTER...(6x)(1)=6x

INNER...(10)(2x)=20x

LAST...(10)(1)=10

 

12x²+6x+20x+10

12x²+26x+10

Answer 2

Alternative solution:

 

12x² + 26x +10 = 2(6x² +13x + 5) = 2*[(2x +1)*(3x + 5)]