SOLUTION: Hello, I am trying to factor an expression. I can't seem to get the right answer. The question is 2x squared minus 7x plus 6. I need to factor the question so it looks something

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hello, I am trying to factor an expression. I can't seem to get the right answer. The question is 2x squared minus 7x plus 6. I need to factor the question so it looks something      Log On


   

Question 262390: Hello, I am trying to factor an expression. I can't seem to get the right answer. The question is 2x squared minus 7x plus 6. I need to factor the question so it looks something like this 2(x+1)(x-6) I can't figure it out thanks.
Found 2 solutions by drk, richwmiller:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We need to factor
2x%5E2+-+7x+%2B+6
this can be factored into
%282x-3%29%28x-2%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Watch carefully as you learn how to factor.
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression 2x%5E2-7x%2B6, we can see that the first coefficient is 2, the second coefficient is -7, and the last term is 6.



Now multiply the first coefficient 2 by the last term 6 to get %282%29%286%29=12.



Now the question is: what two whole numbers multiply to 12 (the previous product) and add to the second coefficient -7?



To find these two numbers, we need to list all of the factors of 12 (the previous product).



Factors of 12:

1,2,3,4,6,12

-1,-2,-3,-4,-6,-12



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



These factors pair up and multiply to 12.

1*12 = 12
2*6 = 12
3*4 = 12
(-1)*(-12) = 12
(-2)*(-6) = 12
(-3)*(-4) = 12


Now let's add up each pair of factors to see if one pair adds to the middle coefficient -7:



First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7




From the table, we can see that the two numbers -3 and -4 add to -7 (the middle coefficient).



So the two numbers -3 and -4 both multiply to 12 and add to -7



Now replace the middle term -7x with -3x-4x. Remember, -3 and -4 add to -7. So this shows us that -3x-4x=-7x.



2x%5E2%2Bhighlight%28-3x-4x%29%2B6 Replace the second term -7x with -3x-4x.



%282x%5E2-3x%29%2B%28-4x%2B6%29 Group the terms into two pairs.



x%282x-3%29%2B%28-4x%2B6%29 Factor out the GCF x from the first group.



x%282x-3%29-2%282x-3%29 Factor out 2 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-2%29%282x-3%29 Combine like terms. Or factor out the common term 2x-3



===============================================================



Answer:



So 2%2Ax%5E2-7%2Ax%2B6 factors to %28x-2%29%282x-3%29.



In other words, 2%2Ax%5E2-7%2Ax%2B6=%28x-2%29%282x-3%29.



Note: you can check the answer by expanding %28x-2%29%282x-3%29 to get 2%2Ax%5E2-7%2Ax%2B6 or by graphing the original expression and the answer (the two graphs should be identical).