How would I factor these equations?
1. 6x² + 3x = 0
2. -2x² + 5x + 3 = 0
I know how to factor equations without the number before x². But when the number is there I don't know how to factor it.
for the second, in general we use what we call the AC-method to factor, if possible, a quadratic in which the coefficient of the squared term is not 1. but for small numbers like 2, we can use trial and error, it would generally be a lot simpler.
now in the place of and , you want numbers that multiply to give you -3, but and will add to give -5
we want to factor out the lowest powers of all things common. i have common to both terms, and i have common to both terms. there is a in the second term, but i can't factor that out, because i only have in the first term. so and are common to both terms, both terms have them, so i will factor out , to get:
so i took out the from the 3, and i have none left in the brackets. as for the , i took out the and one of the 's, so i am left with one on the inside, hence the
now you have,
i told you that is common to both, so factor it out