Question 153035: When factoring the following by the reverse FOIL method, the factors of 6 must add up to the value of B in f(x) = x^2 + Bx + 6; what are the possible values of B? @ The factors of 6 represent the outers and the inners that combine to give the middle term in the trinomial. However, since 6 is positive, B could be positive or negative.
a. 5, 7
b. ±5, ±7
c. -5, 7
d. None of the above, the factors of B must add up to 6
Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First, list the 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)
Now take each pair of numbers and add them together:
| First Number | Second Number | Sum | | 1 | 6 | 1+6=7 | | 2 | 3 | 2+3=5 | | -1 | -6 | -1+(-6)=-7 | | -2 | -3 | -2+(-3)=-5 |
So the possible values of B are 7, 5, -7, and -5 which means that the answer is b. ±5, ±7
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website! There are four factors of 6.
They are 1,2,3,6. You also have to allow for the fact that (-2)*(-3) and (-1)*(-6) also equal 6.
Find the pairs of factors that provide a product that is 6. Then add those factors to find 'B" in the equation.
2+3 = 5
-2 -3 = -5
1 + 6 = 7
-1 -6 = -7
Answer B
Be careful not to generalize this process. It works whenever the coefficient of the x^2 equals 1 (like in this case). In the case where the coefficient of the x^2 is not 1, then the process for finding B is a bit more complicated.
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