SOLUTION: x^2 – 16x + 63

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Question 143273: x^2 – 16x + 63

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to factor?







Looking at x%5E2-16x%2B63 we can see that the first term is x%5E2 and the last term is 63 where the coefficients are 1 and 63 respectively.

Now multiply the first coefficient 1 and the last coefficient 63 to get 63. Now what two numbers multiply to 63 and add to the middle coefficient -16? Let's list all of the factors of 63:



Factors of 63:
1,3,7,9,21,63

-1,-3,-7,-9,-21,-63 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 63
1*63
3*21
7*9
(-1)*(-63)
(-3)*(-21)
(-7)*(-9)

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


Now which of these pairs add to -16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -16

First NumberSecond NumberSum
1631+63=64
3213+21=24
797+9=16
-1-63-1+(-63)=-64
-3-21-3+(-21)=-24
-7-9-7+(-9)=-16



From this list we can see that -7 and -9 add up to -16 and multiply to 63


Now looking at the expression x%5E2-16x%2B63, replace -16x with -7x%2B-9x (notice -7x%2B-9x adds up to -16x. So it is equivalent to -16x)

x%5E2%2Bhighlight%28-7x%2B-9x%29%2B63


Now let's factor x%5E2-7x-9x%2B63 by grouping:


%28x%5E2-7x%29%2B%28-9x%2B63%29 Group like terms


x%28x-7%29-9%28x-7%29 Factor out the GCF of x out of the first group. Factor out the GCF of -9 out of the second group


%28x-9%29%28x-7%29 Since we have a common term of x-7, we can combine like terms

So x%5E2-7x-9x%2B63 factors to %28x-9%29%28x-7%29


So this also means that x%5E2-16x%2B63 factors to %28x-9%29%28x-7%29 (since x%5E2-16x%2B63 is equivalent to x%5E2-7x-9x%2B63)



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Answer:
So x%5E2-16x%2B63 factors to %28x-9%29%28x-7%29