#### Conaanaa

##### New member
I need help factoring ax² + bx + c

Here's an example problem I have...

2x² - 15x + 7

I used http://www.helpalgebra.com/onlinebook/f ... ouping.htm to try and solve it but here's what I got...

WORK -------------
2x² - 15x + 7
2x² - 14x - 1x + 7
(2x² - 14x) + (-x + 7)
x(2x - 14) + (-x + 7)

WORK -------------

Now I am stuck and I don't know what to do. Help, please!

I've tried several other problems on my homework and I can't figure out any of them! Please help, thanks!

#### soroban

##### Elite Member
Hello, Conaanaa!

Your factoring is incomplete . . .

$$\displaystyle 2x^2\,-\,15x\,+\,7$$

Work:
$$\displaystyle 2x^2\,-\,15x\,+\,7$$
$$\displaystyle 2x^2\,-\,14x\,-\,1x\,+\,7$$
$$\displaystyle (2x^2\,-\,14x) \,+\,(-x\,+\,7)$$
$$\displaystyle x(2x\,-\,14)\,+\.(-x\,+\,7)\;$$ <-- here!

The first two terms are: $$\displaystyle \,2x^2\,-\,14x$$

. . Factor completely: $$\displaystyle \,2x(x\,-\,7)$$

The last two terms are: $$\displaystyle \,-x\,+\,7$$

. . It doesn't factor, but we can take out -1: $$\displaystyle \,-1(x\,-\,7)$$

And we have: $$\displaystyle \,2x\underbrace{(x\,-\,7)}\,-\,1\underbrace{(x\,-\,7)}$$
. . . . . . . . . . . . . . . $$\displaystyle \nwarrow$$
There!$$\displaystyle \nearrow\;$$

Take out the common factor: $$\displaystyle \,(x\,-\,7)(2x\,-\,1)$$

#### Conaanaa

##### New member
Oh, wow I see! Thanks for the help!