I don't understand how this expression was factored

I have to factor:
3x^2+17x+10, and my friend is telling me that it factors to (3x + 2)(x + 5).

She's very smart, so i have a good feeling she's right, but she's kind of bad explaining to me why it's correct, and I'd like to know how she got (3x + 2)(x + 5), because I thought the two numbers (without the 'x') had to ADD UP to 17, and multiplied to 10...5+2 doesn't add up to 17, so...what am I missing exactly? >_<

Please help.

3x^2+17x+10

Multiply the 3 and the 10 to get 30. Now ask this question. What two numbers multiply to give 30 but can add to give 17? Well 15 x 2 fit. Now rewrite the equation so the middle term is split up like this:

3x^2 + 15x + 2x + 10 Now put brackets around the terms like this:

(3x^2 + 15x)(2x + 10) Now FACTOR each bracket like this:

3x(x + 5) +2(x + 5) Notice you have two (x + 5)'s? Well that is ONE of the factors, The other is 3x + 2

So now you have (3x + 2)(x + 5)

ax^2 +bx + c

your rule works if a=1.

Try this:

change the equation to x^2 +bx + a*c and do what you are used to.

You will get x^2 + 17x + 30

Your answers will be +2 and +15

Now divide each of these by a (in this case, 3)

you get 2/3 and 5
or
(x+2/3)(x+5)

multiply the (x+2/3) term by 3 to get rid of the denominator and you get (3x+2)

so the factors are (3x+2)(x+5)

look here for a good tutorial:
http://www.youtube.com/watch?v=ZQ-NRsWhO…

Factoring is very easy and I'm very sure that you'll be able to factor it next time on your own check the slides in the link below

And yes, she's right the answer is (x+5)(3x+2)

http://www.mathsisfun.com/algebra/factor…

3x*x = 3x^2
3x*5 = 15x
2*x = 2x
2*5 = 10
Add RHS 3x^2+15x+2x+10 =
3x^2+17x+10