# factoring

#### denise

##### New member
hello i need help factoring this basic factoing problem

4x^(2) + x - 6

are u supposed to take out the four or can u just have

( 2x + ?)(2x + ?)

#### Matt

##### Junior Member
Hi Denise,

Whenever the coefficient of x<sup>2</sup> is something other than 1, there can be more than one possibility. In this case, it could either be:

. . . . (2x + ?)(2x + ?)

or:

. . . . (4x + ?)(x + ?)

Definitely try both possibilities when you go to factor this polynomial.

#### denise

##### New member
ok. i understand that but i cant find the two numbers that goes in the ()s. i know that is one of the multiples of the last number and has to add to get the middle number but i am having trouble findin thouse two numbers

G

#### Guest

##### Guest
This one cannot be factored nicely. ax<sup>2</sup> + bx + c can be factored nicely iff b<sup>2</sup> - 4ac is a perfect square. For your trinomial,

b<sup>2</sup> - 4ac
= 1<sup>2</sup> - 4 * 4 * (-6)
= 1 + 96
= 97

which is not a perfect square. You could use the quadratic formula to factor this, or you might just say it's "prime".