SOLUTION: I have two questions if that's okay... 1. Can you show me, step by step, how to find the factors of x^2 – 5x – 6 2. Can you show me, step by step, how to find the

Question 145795: I have two questions if that's okay...
1. Can you show me, step by step, how to find the factors of x^2 – 5x – 6
2. Can you show me, step by step, how to find the factors of x^2 – x – 20
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Looking at we can see that the first term is and the last term is 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 Number	Second Number	Sum
1	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-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 , 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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Answer:
So factors to

# 2

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -20 respectively.

Now multiply the first coefficient 1 and the last coefficient -20 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient -1? Let's list all of the factors of -20:

Factors of -20:
1,2,4,5,10,20

-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -20
(1)*(-20)
(2)*(-10)
(4)*(-5)
(-1)*(20)
(-2)*(10)
(-4)*(5)

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

Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1

First Number	Second Number	Sum
1	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

From this list we can see that 4 and -5 add up to -1 and multiply to -20

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

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SOLUTION: I have two questions if that's okay... 1. Can you show me, step by step, how to find the factors of x^2 &#8211; 5x &#8211; 6 2. Can you show me, step by step, how to find the

SOLUTION: I have two questions if that's okay... 1. Can you show me, step by step, how to find the factors of x^2 – 5x – 6 2. Can you show me, step by step, how to find the