## anonymous 5 years ago factor completely: 25s^2+4-20s

1. Mohsen

(5x-2)(5x-2) x=2/5

2. Mohsen

sorry,not x but s

3. mathteacher1729

As a general technique for solving these problems, we know we want our answer to look like ( stuff ) * (stuff) , to be more specific, we want it to look like ( number* s plus/minus number) * ( number*s plus/minus number). In this case you can see that the 25 multiplied by s^2 can factor only into 5*5 or 1*25. (that's where the 5x comes from). From there it's filling in the steps of FOIL.

4. anonymous

hold the phone. it says "factor" not solve for x. you do not have an equation here so do not write x = anything!

5. mathteacher1729

I would recommend checking out these videos: http://www.mathtv.com go to algebra > quadratic equation > factoring polynomials, and watch all the ones with the old guy. He is awesome. :D

6. Mohsen

the value of s just an extra...

7. anonymous

it would help to write as $25s^2-20s+4$ and recognize this as a "perfect square"

8. anonymous

$25s^2$ is the square of $5s$ 4 is the square of -2 and $-20x =2\times -2\times 5x$

9. anonymous

so right away you get $(5x-2)^2$ because $(a-b)^2=a^2-2ab+b^2$

10. mathteacher1729

There is a nice illustration of that here: http://en.wikipedia.org/wiki/File:A_plus_b_au_carre.svg

11. mathteacher1729

Oh for goodness sake... http://upload.wikimedia.org/wikipedia/commons/c/c2/A_plus_b_au_carre.svg