Which is a factor of 12x^2– 46x – 8 ?

Answers: 3x – 2
3x – 4
2x + 1
2

Question

Which is a factor of 12x^2– 46x – 8 ?

Answers:    3x – 2 
                  3x – 4 
                  2x + 1 
                  2

msmr · Answer

$$12x ^{2} - 46x - 8$$

Quadratic equations like this one are always in the format $$ax ^{2} + bx + c$$
To factor these problems, you multiply a and c, and take factors of that number that sum to b.

In this problem, a = 12, b = 46, and c = -8.
$$a*c = 12 * -8 = -96$$

The factors of -96 that sum to 46 are 48 and -2 (48-2 = 46)

Then, you split the middle term into the factors:

$$12x ^{2} + 48 x - 2x - 8$$

Then, you group the first two terms and the last two terms and factor them separately:
$$12x(x + 4) -2(x+4)$$
 
The factors would be: (12x - 2)(x+4). To factor this even further, you factor out a 2 from the first term: 2(6x-1)(x+4)

So, the only factor in your list that applies to this problem would be 2.