SOLUTION: i need to factor these. {{{x^2-5x-6}}} & {{{4x^2-8x+4}}} please help fast! :] thanks.

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Question 143169: i need to factor these.
x%5E2-5x-6
&
4x%5E2-8x%2B4
please help fast!
:]
thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



Looking at 1x%5E2-5x-6 we can see that the first term is 1x%5E2 and the last term is -6 where the coefficients are 1 and -6 respectively.

Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient -5? 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, the product of a negative and a positive number is a negative number


Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5

First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1



From this list we can see that 1 and -6 add up to -5 and multiply to -6


Now looking at the expression 1x%5E2-5x-6, replace -5x with 1x%2B-6x (notice 1x%2B-6x adds up to -5x. So it is equivalent to -5x)

1x%5E2%2Bhighlight%281x%2B-6x%29%2B-6


Now let's factor 1x%5E2%2B1x-6x-6 by grouping:


%281x%5E2%2B1x%29%2B%28-6x-6%29 Group like terms


x%28x%2B1%29-6%28x%2B1%29 Factor out the GCF of x out of the first group. Factor out the GCF of -6 out of the second group


%28x-6%29%28x%2B1%29 Since we have a common term of x%2B1, we can combine like terms

So 1x%5E2%2B1x-6x-6 factors to %28x-6%29%28x%2B1%29


So this also means that 1x%5E2-5x-6 factors to %28x-6%29%28x%2B1%29 (since 1x%5E2-5x-6 is equivalent to 1x%5E2%2B1x-6x-6)



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Answer:
So x%5E2-5x-6 factors to %28x-6%29%28x%2B1%29





# 2




4x%5E2-8x%2B4 Start with the given expression


4%28x%5E2-2x%2B1%29 Factor out the GCF 4


Now let's focus on the inner expression x%5E2-2x%2B1




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Looking at 1x%5E2-2x%2B1 we can see that the first term is 1x%5E2 and the last term is 1 where the coefficients are 1 and 1 respectively.

Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient -2? Let's list all of the factors of 1:



Factors of 1:
1

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

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

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


Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

First NumberSecond NumberSum
111+1=2
-1-1-1+(-1)=-2



From this list we can see that -1 and -1 add up to -2 and multiply to 1


Now looking at the expression 1x%5E2-2x%2B1, replace -2x with -1x%2B-1x (notice -1x%2B-1x adds up to -2x. So it is equivalent to -2x)

1x%5E2%2Bhighlight%28-1x%2B-1x%29%2B1


Now let's factor 1x%5E2-1x-1x%2B1 by grouping:


%281x%5E2-1x%29%2B%28-1x%2B1%29 Group like terms


x%28x-1%29-1%28x-1%29 Factor out the GCF of x out of the first group. Factor out the GCF of -1 out of the second group


%28x-1%29%28x-1%29 Since we have a common term of x-1, we can combine like terms

So 1x%5E2-1x-1x%2B1 factors to %28x-1%29%28x-1%29


So this also means that 1x%5E2-2x%2B1 factors to %28x-1%29%28x-1%29 (since 1x%5E2-2x%2B1 is equivalent to 1x%5E2-1x-1x%2B1)


note: %28x-1%29%28x-1%29 is equivalent to %28x-1%29%5E2 since the term x-1 occurs twice. So 1x%5E2-2x%2B1 also factors to %28x-1%29%5E2



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So our expression goes from 4%28x%5E2-2x%2B1%29 and factors further to 4%28x-1%29%5E2


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Answer:

So 4x%5E2-8x%2B4 factors to 4%28x-1%29%5E2