Question

Factor the expression-15x^2-24x

Answer 1

you have to look at common numbers that can be taken out of each term to factor it. first we look at -15x^2 and -24x.

notice both -15 and -24 can be divided by -3. so i can dive both by -3 and get
(5x^2 + 8x)

but the -3 has to go somewhere. it does not just disappear. so i put it at the front like so:
-3(5x^2 + 8x)

now we have to consider the x^2 and x. x is not a particular number. it is a domain of numbers. so it is also possible to divide both of these numbers by x. if i do that and put x at the front i get:
-3(x)(5x + 8)

this is your answer. you can checm it by multiplying it out.

another way to look at this is by seperating the terms (-15x^2) and (-24x) and putting them into their prime factors. like so:
(-15x^2)
(-)(3 * 5 * x * x)

and:
(-24x)
(-)(3 * 2 * 2 * 2 * x)

when we look at them like this we can pull out their common factors more easily. we can clearly see they share factors of 3 and x. they also share a negative sign. so i can pull those out to the front and keep whatever is left in parenthesis like this:
(-3x) and. (5 * x) and(2 * 2 * 2)

wotk out math and know they are both positive now since we removed the negative sign.
(-3x)(5x + 8)

Answer 2

Since there is no constant, you can look for common factors using the diamond method or any method that works for you. A common factor for both is 3x, so factor it out. The final answer is 3x(-5x-8).