How do you factor #y= 3x^2+29x-44 # ?
The explanation below shows one method on how to factor polynomials when the leading coefficient is not equal to 1.
Here's one way to factor a polynomial when the leading coefficient not equal to 1:
Start by finding 2 numbers
In this case
It usually helps to think of the prime factors of the number.
In this case, they are:
You can try a few combinations, keeping in mind that, in this case, the 2 numbers must add to
The winning combination turns out to be
Now write down the current answers as if they were the factors:
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,
If they can be divided evenly, leave it at that. If not, move the denominator as a factor next to the x, like this:
And those are the factors!