3x squared minus 7x equals 0
in my math homework...solve the quadratic equations by factoring
3x^2 - 7x = 0
When we factor this, we will have:
(3x + a)(x + b) = 0
We need an a and b such that 3b + a = -7, and ab = 0.
We know ab has to equal zero, because there is no constant
term following the 7x.
If we set a = 0 and b = -7/3, we will have what we are looking for.
(3x + 0)(x - 7/3) = 0
Multiply that out, and we get:
3x^2 + 0x - 3(7/3)x - 0 = 0
3x^2 + 0x - 7x - 0 = 0
3x^2 - 7x = 0, which is what we started with.