factoring

[denise]

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]

Hi Denise,

Whenever the coefficient of x² 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]

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

 

[Guest]

This one cannot be factored nicely. ax² + bx + c can be factored nicely iff b² - 4ac is a perfect square. For your trinomial,

b² - 4ac
= 1² - 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".