SOLUTION: Factorize 3ax^2+7ax + 2a

Question 167732: Factorize
3ax^2+7ax + 2a
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

------------------------------------------------------------

Looking at we can see that the first term is and the last term is where the coefficients are 3 and 2 respectively.

Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient 7? Let's list all of the factors of 6:

Factors of 6:
1,2,3,6

-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)

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

Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7

First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

From this list we can see that 1 and 6 add up to 7 and multiply to 6

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 )

------------------------------------------------------------

So our expression goes from and factors further to

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

So factors to

RELATED QUESTIONS
factorize completely the expression abx^2 +6y-3ax-2byx (answered by MathLover1)

Factorize... (answered by MathLover1)

ax^2-7ax+12a (answered by swincher4391)

3ax+6=a^2x+2a= (answered by jim_thompson5910)

3ax^2 - 12a^2x^4 /... (answered by stanbon)

factorize : (b+2a)� -... (answered by Edwin McCravy)

Hi The Q is: Find the sum of 1.) 5x^2,3ab,-2ab, -4a^2,5ab,-2a^2 2.)... (answered by Alan3354)

ax+bx=a^2+2ab+b^2= 3ax+6=a^2x+2a= 4x-4=b^2+5b-bx=... (answered by user_dude2008)

Please solve: (x^2-ax+b)is a factor of x^3+3ax^2+3bx+c Show that b=-2a^2 (answered by CharlesG2)