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Factor Binomials: -3x^2+7x Answered

Kumon's Math Study Guide provides this question:

Know how to "factor" Binomials:
Problem: -3x^2 + 7x
Answer: 0, 7/3

I thought the obvious answer is pulling out the x for the original binominal which would result in x (-3x+7)

Although I haven't seen this before, I could take each of the factors and have them equal zero to come up with the answer. Am I missing something?

Example: x = 0 and -3x + 7 = 0
Solve for x, x = 0 and x = 7/3


Nope. That's exactly right. You have found the roots of the equation.

Life gets much more interesting when you have the full quadratic expression ax^2+bx+c=0 I sincerely hope that Kumon doesn't force you to factor them by hand. I found Kumon depressingly repetitive, and my kids didn't like it at all.


The next question has me completely stumped:
Factor Trinomials:
Problem: 6x^2 + 15x + 6
Answer: -1/2, -2

So I know you can factor 3 our of the trinomial:
3 (2x^2 + 5x +2)

I suppose I can ignore the 3 and go thought the same process of assuming that the expression equals zero.
2x^2 + 5x + 2 = 0
2x^2 +5x = -2
x (2x +5) = -2
so x = -2 but I do not know how to get the -1/2
     -What am I missing?

I am still stumped if I leave the 3 in the trinomial:

6x^2 + 15x + 6 = 0
6x^2 + 15x = -6
3x (x +5) = -6

3x = -6
x = -2

x + 5 = -6
x = -11

Answer: -2, -11 ???

There is a formula for solving quadratic equations, which are of the form ax^2+bx+c=0 - which these are.

The roots are -b +/- sqrt(b^2-4ac) /2a

Take the coefficients of your equation - here, a=6, b=15, c=6
Divide throughg them in.