I have a factoring question; what is 8a^2-8a-30? I've been working on this for a while and I think I understand factoring, but I'm not getting the right answer, which is supposed to be 2(2a-5)(2a+3).
Any help would be so appreciated! :)
factor 2 out (all coefficents are multiples of 2)
2(4a^2 -4a-15)
Now factor the second part...
2(2a-5)(2a+3)
It might take a while to find the factors
but, I don't understand how you got the answer in the first place; can you place explain?
Of course! I'd be happy to help you with factoring the expression 8a^2 - 8a - 30.
To factor this expression, we need to look for common factors first, if any. In this case, there is no common factor among all three terms.
To factor a trinomial like this, we need to write it in the form of (x + m)(x + n), where m and n are constants.
Let's start by multiplying the coefficient of the leading term (8) with the constant term (-30). In this case, 8 * -30 = -240.
Now, we need to find two numbers whose product is -240 and whose sum is the coefficient of the middle term (-8). In this case, the two numbers are -20 and 12. If we add -20 and 12, we get -8.
So, we rewrite the middle term (-8a) as -20a + 12a.
Now, we can factor the expression:
8a^2 - 20a + 12a - 30
We group the terms:
(8a^2 - 20a) + (12a - 30)
Next, we factor out the greatest common factor from each group:
4a(2a - 5) + 6(2a - 5)
Notice that we have a common binomial factor of (2a - 5) in both terms.
We can now combine the two terms:
4a(2a - 5) + 6(2a - 5) = (4a + 6)(2a - 5)
Finally, we can further simplify the expression by factoring out a common factor of 2 from the first term:
(4a + 6)(2a - 5) = 2(2a + 3)(2a - 5)
Therefore, the factored form of 8a^2 - 8a - 30 is 2(2a + 3)(2a - 5).
I hope this explanation helps you understand the factoring process! Let me know if you have any more questions.