SOLUTION: State which method should be applied as the first step for factoring the polynomial 2a2 + 9a + 10. Thank you for your help in solving this problem. Daniel H. Jack

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Question 1015316: State which method should be applied as the first step for factoring the polynomial 2a2 + 9a + 10.
Thank you for your help in solving this problem.
Daniel H. Jack
Found 2 solutions by FrankM, Theo:
Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
2a%5E2+%2B+9a+%2B+10
The quadratic equation is always a fallback. But factoring is pretty cool.
What number adds to 9, but multiplies to 20? (note 20 is the product of 2 and 10, A*C)

2a%5E2+%2B+4a+%2B+5a+%2B+10 << -- we split that middle term.
2a+%2A+%28a%2B2%29+%2B+5%28a+%2B+2%29
%282a%2B5%29%28a%2B2%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you probably want to set it equal to 0 to put it in standard form.

it would then be 2a^2 + 9a + 10 = 0

you would then want to factor out the greatest common factor.

since you can't, you would then try to see if you can factor it.

the factoring method i would try to use is splitting the middle term method, for want of a better name.

start with 2x^2 + 9x + 10 = 0

i replaced a with x because it's more of a standard equation that way.

multiply the coefficient of the x^2 term by the constant term to get 2 * 10 = 20

find the possible factors of 20 that add up to 9.

possible factors are 1*20, 2*10, 4*5 *****

4*5 is the one that you want because 4 + 5 = 9.

now is where you split the middle term.

9x = 4x + 5x, so the equation becomes:

2x^2 + 5x + 4x + 10 = 0

now group the first 2 terms and factor out the greatest common factor from them to get:

x * (2x + 5) + 4x + 10 = 0

now factor the second group of 2 terms so that one of those factors is (2x + 5).

you will get x * (2x + 5) + 2 * (2x + 5) = 0

now factor out the common term of (2x + 5) to get (x + 2) * (2x + 5) = 0

your factored equation will be (x+2) * (2x+5)= 0

you can confirm this is correct by distributing the multiplication to get (x+2) * (2x+5) = 2x^2 + 5x + 4x + 10 which = 2x^2 + 9x + 10 after you combine like terms.

so you factored it correctly and your factored equation is y = (x+2) * (2x + 5).

if you want a tutorial on factoring, see the following:

http://www.purplemath.com/modules/solvquad.htm

and the following:

http://www.purplemath.com/modules/factquad.htm

they're both good.

try the second one first.
if you still need to, then try the first.
the splitting the middle term method is similar to the box method without the box.