How do you factor y=3x2+29x44 ?

1 Answer
Jun 7, 2018

(x+11)(3x4)
The explanation below shows one method on how to factor polynomials when the leading coefficient is not equal to 1.

Explanation:

Here's one way to factor a polynomial when the leading coefficient not equal to 1:

For: y=ax2+bx+c
Start by finding 2 numbers x1 and x2 where:
x1x2=ac
and
x1+x2=b

In this case ac=3(44)=132

It usually helps to think of the prime factors of the number.
In this case, they are: 132=22311
You can try a few combinations, keeping in mind that, in this case, the 2 numbers must add to 29.
The winning combination turns out to be 33 and 4
33(4)=132
33+(4)=29

Now write down the current answers as if they were the factors:
(x+33)(x4)

However, that's not quite the answer yet. If we left it like this, the leading coefficient would be 1 and the last coefficient would be too big. So we need to adjust for that.

Divide the 2 answers by the leading coefficient, in this case, 3.

(x+333)(x43)
If they can be divided evenly, leave it at that. If not, move the denominator as a factor next to the x, like this:

(x+11)(3x4)

And those are the factors!