My daughter has some homework problems that I cannot help her with. The instructions say to FACTOR: Show you work.

1. 4x squared +19x-5

2. 16x squared -81y squared

3. y to the fifth power + 32x to the fifth power

Can anyone out there help with explaining this?

Thanks!

I will help with the first, then you all try the others. OK?



When you have a quadratic in the form

Find two numbers when mutiplied equal ac and when added equal b.

In your case:

What two numbers when multiplied equal -20(because (-5)(4)=-20) and when added equal 19?

How about 20 and -1. 20 + (-1)=19 and (20)(-1)=-20.

Replace 19 with the 20 and -1:



Group:



Factor out something common from both sets of parentheses:



See? What is in the parentheses is the same. That is essential to factoring properly.

Now, we have

And we're done.