SOLUTION: How do you factor b� -20b+51 ?

Question 117766: How do you factor b� -20b+51 ?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 51 respectively.

Now multiply the first coefficient 1 and the last coefficient 51 to get 51. Now what two numbers multiply to 51 and add to the middle coefficient -20? Let's list all of the factors of 51:

Factors of 51:
1,3,17,51

-1,-3,-17,-51 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 51
1*51
3*17
(-1)*(-51)
(-3)*(-17)

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

Now which of these pairs add to -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20

First Number	Second Number	Sum
1	51	1+51=52
3	17	3+17=20
-1	-51	-1+(-51)=-52
-3	-17	-3+(-17)=-20

From this list we can see that -3 and -17 add up to -20 and multiply to 51

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

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