Help me help my son...factoring expressions question

[deerluvr]

I've been out of school too long! Can someone please explain how to solve this equation: 3x^2 - 10x +8

If I can understand one problem I can probably help him with the other 16. He was able to solve the first 40 questions but the 3x^2 has us both stumped. Would really appreciate any help!!

Thanks much!

 

[stapel]

Can someone please explain how to solve this equation: 3x^2 - 10x +8

Your subject line mentions "factoring expressions", but you say (above) that you need to solve an equation (something with an "equals" in it). But you've posted an expression. Are you supposed to be factoring...?

Did all the other expressions/equations have a plain "x²" for the leading term?

Thank you.

Eliz.

 

[Gene]

(3x+a)(x+b) =
3x²+(a+3b)x+ab = 3x²-10x+8
so a+3b=-10
ab=8
The factors of 8 are 8,4,2,1.
Since they add to -10 at least one must be negative.
Since they multiply to +8 both must be negative.
-8*-1 or -2*-4 are the two possibilities. Try them in a+3b = -10
-8+3*-1 = -11 nope
-1+3*-8 = -25 nope
-2+3*-4 = -14 nope
-4+3*-2 = -10 hoorah.
a=-4 and b = -2
The factors are
(3x-4)(x-2)

This assumes you have not yet met the quadratic formula.