SOLUTION: what is equal to x^2-5x+6? a. (x-2) (x-3) b. (x-2) (x+3) c. (x+6) (x-1) d. (x-6) (x+1) i think the answer is A but I wanted make sure.. thanks :o)

Algebra ->  Equations -> SOLUTION: what is equal to x^2-5x+6? a. (x-2) (x-3) b. (x-2) (x+3) c. (x+6) (x-1) d. (x-6) (x+1) i think the answer is A but I wanted make sure.. thanks :o)      Log On


   

Question 175031: what is equal to x^2-5x+6?
a. (x-2) (x-3)
b. (x-2) (x+3)
c. (x+6) (x-1)
d. (x-6) (x+1)
i think the answer is A but I wanted make sure.. thanks :o)
Found 2 solutions by jim_thompson5910, actuary:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression x%5E2-5x%2B6, we can see that the first coefficient is 1, the second coefficient is -5, and the last term is 6.


Now multiply the first coefficient 1 by the last term 6 to get %281%29%286%29=6.


Now the question is: what two whole numbers multiply to 6 (the previous product) and add to the second coefficient -5?


To find these two numbers, we need to list all of the factors of 6 (the previous product).


Factors of 6:
1,2,3,6
-1,-2,-3,-6


Note: list the negative of each factor. 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)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -5:


First NumberSecond NumberSum
161+6=7
232+3=5
-1-6-1+(-6)=-7
-2-3-2+(-3)=-5



From the table, we can see that the two numbers -2 and -3 add to -5 (the middle coefficient).


So the two numbers -2 and -3 both multiply to 6 and add to -5


Now replace the middle term -5x with -2x-3x. Remember, -2 and -3 add to -5. So this shows us that -2x-3x=-5x.


x%5E2%2Bhighlight%28-2x-3x%29%2B6 Replace the second term -5x with -2x-3x.


%28x%5E2-2x%29%2B%28-3x%2B6%29 Group the terms into two pairs.


x%28x-2%29%2B%28-3x%2B6%29 Factor out the GCF x from the first group.


x%28x-2%29-3%28x-2%29 Factor out 3 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-3%29%28x-2%29 Combine like terms. Or factor out the common term x-2

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Answer:


So x%5E2-5x%2B6 factors to %28x-3%29%28x-2%29.


This means that x%5E2-5x%2B6=%28x-3%29%28x-2%29



Note: you can check the answer by FOILing %28x-3%29%28x-2%29 to get x%5E2-5x%2B6 or by graphing the original expression and the answer (the two graphs should be identical).

Answer by actuary(112) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct.
You could test the possible answers by multiplying the factors in the factorizations and seing which one matches the initial equation.