SOLUTION: 40x^2-48x-88

Question 193101: 40x^2-48x-88
Found 2 solutions by jim_thompson5910, josmiceli:
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

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Looking at we can see that the first term is and the last term is where the coefficients are 5 and -11 respectively.

Now multiply the first coefficient 5 and the last coefficient -11 to get -55. Now what two numbers multiply to -55 and add to the middle coefficient -6? Let's list all of the factors of -55:

Factors of -55:
1,5,11,55

-1,-5,-11,-55 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -55
(1)*(-55)
(5)*(-11)
(-1)*(55)
(-5)*(11)

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

Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6

First Number Second Number Sum
1 -55 1+(-55)=-54
5 -11 5+(-11)=-6
-1 55 -1+55=54
-5 11 -5+11=6

From this list we can see that 5 and -11 add up to -6 and multiply to -55

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 )

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So our expression goes from and factors further to

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Answer:

So completely factors to

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

(I assume you want the roots)
Use quadratic equation

The 2 roots are:

and

I checked these answers - OK
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