Expert: David Montiel - 8/27/2009

Question
I'm having some trouble with factoring. I got stuck with this problem 20x^2-93x-34. Can you please help me? Thank you.

Answer
Hello Stephanie,

You can always factor an expression like the one above into the form:

(cx+b)(cx+a)

However it seems like your expression cannot be written in that form (I tried) with integer values a, b and c. But when you have a second degree polynomial, you can always apply the formula:

x1,x2=(-b +- sqrt(b^2-4ac))/(2a)                         ("sqrt" means "square root of")

Let me explain this a little. When you have an equation

ax^2+bx+c=0

the solutions x1, x2, are the values of "x" that make the left hand side zero. This means that the same equation can be written

(x-x1)(x-x2)=0

When you take the product you get

x^2 -(x1+x2)x + x1x2 = 0

Notice that the left hand side has (almost) the form of your expression:

20x^2-93x-34

except for the factor of 20. So all you need to do is find x1 and x2 and multiply the product (x-x1)(x-x2)
by 20. The answer will look like:

20(x-x1)(x-x2)

In your case, the numbers x1 and x2 will not be integers.

I hope this is clear, but please let me know if it isn't.

Cheers,
David