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?

4x^{2}+19x-5

When you have a quadratic in the form ax^{2}+bx+c

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:

4x^{2}+20x-x-5

Group:

(4x^{2}+20x)-(x+5)

Factor out something common from both sets of parentheses:

4x(x+5)-(x+5)

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

Now, we have (4x-1)(x+5)

And we're done.