SOLUTION: Factor 4x^2+16x-48

Question 190281: Factor
4x^2+16x-48
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 1 and -12 respectively.

Now multiply the first coefficient 1 and the last coefficient -12 to get -12. Now what two numbers multiply to -12 and add to the middle coefficient 4? Let's list all of the factors of -12:

Factors of -12:
1,2,3,4,6,12

-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -12
(1)*(-12)
(2)*(-6)
(3)*(-4)
(-1)*(12)
(-2)*(6)
(-3)*(4)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4

First Number	Second Number	Sum
1	-12	1+(-12)=-11
2	-6	2+(-6)=-4
3	-4	3+(-4)=-1
-1	12	-1+12=11
-2	6	-2+6=4
-3	4	-3+4=1

From this list we can see that -2 and 6 add up to 4 and multiply to -12

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 completely factors to

RELATED QUESTIONS
Factor: 4x^2 - 16x -... (answered by tommyt3rd)

Factor Completely: x^2+16x+48 Thanks... (answered by tutorcecilia)

Factor. Check by multiplying... (answered by Fombitz)

Factor 4x^2-28x+48... (answered by solver91311,jim_thompson5910)

Factor these ? 4x^2 -12x -40 2x^2 -16x +30 (answered by Gator Tutoring,jim_thompson5910)

how to factor completely: 16x^2 + 4x - 2 =... (answered by richwmiller)

Factor completely:... (answered by galactus)

Factor by grouping... (answered by cutepiscean5)

how can I factor... (answered by jim_thompson5910)