SOLUTION: Could you please help me solve the following problem: Factor these three examples completely. Remember to check for common factors first. Some questions will require two types o

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Question 839487: Could you please help me solve the following problem:
Factor these three examples completely. Remember to check for common factors first. Some questions will require two types of factoring.
a) 2a^2 - 5a - 3
b) 4(x + y) - 3m(x + y)
c) 2a^2 + 24a + 40
Thank you!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Part (a) appears to be the only troubling one.

Try this:
%282a%2B-+what%29%28a%2B-+whatelse%29
You want to find combinations of "what" and "whatelse" which will give product of -3 and after doing the binomial multiplications gives sum of -5.

Try 1, -3:
%282a%2B1%29%28a-3%29---<--------This is the answer, factored.
2a%5E2%2Ba-6a-3
highlight_green%282a%5E2-5a-3%29 ----- the given expression to be factored.
GOOD. This one works.
Answer: highlight%28%282a%2B1%29%28a-3%29%29


What happens if you tried the other combinations...

Try -1, 3:
(2a-1)(a+3)
2a^2-1a+6a-3
2a^2+5a-3
No good.

Try 3, -1:
(2a+3)(a-1)
2a^2+3a-2a-3
2a^2+a-3
No good.

Try -3, 1:
(2a-3)(a+1)
2a^2-3a+2a-3
2a^2-a-3