How do you factor #25x^2-10x-15#?

Question

Nathan Axel · Accepted Answer

#25x^2-10x-15 = 5(x-1)(5x+3)#

First note that all of the terms are divisible by #5# so separate that out as a factor first:

#25x^2-10x-15 = 5(5x^2-2x-3)#

Next notice that the sum of the coefficients of the remaining factor is zero. That is: #5-2-3 = 0#. So #x=1# is a zero and #(x-1)# a factor:

#5x^2-2x-3 = (x-1)(5x+3)#

Putting it all together:

#25x^2-10x-15 = 5(x-1)(5x+3)#

Hazel Anglin · Answer

undefined To factor the expression 25x^2 - 10x - 15, you can use the method of factorization by grouping. First, find two numbers that multiply to give you (25 * -15) = -375 and add to give you -10. Those numbers are -25 and 15. Then, split the middle term using these numbers: 25x^2 - 25x + 15x - 15. Factor by grouping: 25x(x - 1) + 15(x - 1). Factor out the common factor (x - 1): (25x + 15)(x - 1).

Julia Adams · Answer

undefined To factor the expression $25x^2 - 10x - 15$, you can first factor out the greatest common factor, if any. In this case, there is no common factor other than 1. Then, you can use the factoring techniques such as grouping, trial and error, or quadratic formula. However, in this case, you can simplify the expression by factoring out the common factor first, which is 5:

$25x^2 - 10x - 15 = 5(5x^2 - 2x - 3)$

Now, you can factor the quadratic expression $5x^2 - 2x - 3$ using either factoring by grouping, factoring by trial and error, or quadratic formula. In this case, the expression $5x^2 - 2x - 3$ can be factored as follows:

$5x^2 - 2x - 3 = (5x + 3)(x - 1)$

So, the fully factored form of $25x^2 - 10x - 15$ is $5(5x + 3)(x - 1)$.