SOLUTION: 3x^2 + 8x + 5 how would i factor this ?

Question 115652: 3x^2 + 8x + 5 how would i factor this ?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 3 and 5 respectively.

Now multiply the first coefficient 3 and the last coefficient 5 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 8? Let's list all of the factors of 15:

Factors of 15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 15
1*15
3*5
(-1)*(-15)
(-3)*(-5)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8

First Number	Second Number	Sum
1	15	1+15=16
3	5	3+5=8
-1	-15	-1+(-15)=-16
-3	-5	-3+(-5)=-8

From this list we can see that 3 and 5 add up to 8 and multiply to 15

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

-------------------------------
Answer:

So factors to
RELATED QUESTIONS
this is about factoring 3x^2+8x+5 how do i factor... (answered by stanbon)

how do I factor... (answered by fractalier)

I need to factor 8x^3-8x^2-x+1 how do factor this... (answered by mananth)

x-2 ____ 8x^2-32 How do i factor... (answered by vleith)

How would factor... (answered by richwmiller,MathTherapy)

Help please I need to know how to factor this problem... (answered by anjulasahay,funmath)

How would I solve the following? x^2+8x= -16 Also the following: 3x^2=2x+5... (answered by stanbon)

How would you go about solving this factor? Solve: 8x^2 + 2x =... (answered by stanbon)

How would I factor this? {{{12(4x-1)^3(2x+5)^9 +3(4x-1)^4(2x+5)^8}}} My attempt:... (answered by jim_thompson5910)