missionary3
Jan 17, 2008, 10:32 AM
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!
galactus
Jan 18, 2008, 11:10 AM
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.