SOLUTION: It's factoring patterns. I did solve this one, but I am not sure what I did wrong. The problem is x^2+x-6. The answer I got was (x+2)(x-3).
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: It's factoring patterns. I did solve this one, but I am not sure what I did wrong. The problem is x^2+x-6. The answer I got was (x+2)(x-3).
Log On
Question 147453This question is from textbook algebra
: It's factoring patterns. I did solve this one, but I am not sure what I did wrong. The problem is x^2+x-6. The answer I got was (x+2)(x-3). This question is from textbook algebra
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 -6 respectively.
Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient 1? Let's list all of the factors of -6:
Factors of -6:
1,2,3,6
-1,-2,-3,-6 ...List the negative factors as well. 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)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1
First Number
Second Number
Sum
1
-6
1+(-6)=-5
2
-3
2+(-3)=-1
-1
6
-1+6=5
-2
3
-2+3=1
From this list we can see that -2 and 3 add up to 1 and multiply to -6
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 )
(