## anonymous 5 years ago What Is the Factored Form Of Each Expression?16x^2 + 24x + 9 Please Help Me!

1. anonymous

note that the x^2 term and the constant term are both perfect squares. it looks like it might be (4x+3)^2 and a quick check verifies that the middle terms add up to 24x

2. anonymous

Thanks, That's Actually Exactly it! Thanks so Much! =)

3. anonymous

If you have a similar problem doesn't work out nicely, or you don't "just see it", there is a sure fire way to factor a quadratic.

4. anonymous

any quadratic will factor into $k(x-r1)(x-r2)$ where r1 and r2 are called the roots. to find the roots of some quadratic, do the following

5. anonymous

let our quadratic be ax^2+bx+c. Then $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$ For example, in this case a=16, b=24, and c=9 and if you plug those in, it would work out to be -3/4, which is the solution to 16x^2+24x+9=0

6. anonymous

Thank You