SOLUTION: What are the factors of x^2-9x+8?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What are the factors of x^2-9x+8?      Log On


   

Question 195816: What are the factors of x^2-9x+8?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression x%5E2-9x%2B8, we can see that the first coefficient is 1, the second coefficient is -9, and the last term is 8.


Now multiply the first coefficient 1 by the last term 8 to get %281%29%288%29=8.


Now the question is: what two whole numbers multiply to 8 (the previous product) and add to the second coefficient -9?


To find these two numbers, we need to list all of the factors of 8 (the previous product).


Factors of 8:
1,2,4,8
-1,-2,-4,-8


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 8.
1*8
2*4
(-1)*(-8)
(-2)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -9:


First NumberSecond NumberSum
181+8=9
242+4=6
-1-8-1+(-8)=-9
-2-4-2+(-4)=-6



From the table, we can see that the two numbers -1 and -8 add to -9 (the middle coefficient).


So the two numbers -1 and -8 both multiply to 8 and add to -9


Now replace the middle term -9x with -x-8x. Remember, -1 and -8 add to -9. So this shows us that -x-8x=-9x.


x%5E2%2Bhighlight%28-x-8x%29%2B8 Replace the second term -9x with -x-8x.


%28x%5E2-x%29%2B%28-8x%2B8%29 Group the terms into two pairs.


x%28x-1%29%2B%28-8x%2B8%29 Factor out the GCF x from the first group.


x%28x-1%29-8%28x-1%29 Factor out 8 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28x-8%29%28x-1%29 Combine like terms. Or factor out the common term x-1

---------------------------------------------


Answer:


So x%5E2-9x%2B8 factors to %28x-8%29%28x-1%29.


Note: you can check the answer by FOILing %28x-8%29%28x-1%29 to get x%5E2-9x%2B8 or by graphing the original expression and the answer (the two graphs should be identical).