Carcass wrote:
\(24x^2 + bx + c=(dx+e)(fx+g)\)
\(b,c,d,e,f,\) and \(g\) are integers
Quantity A |
Quantity B |
\(d+f\) |
\(26\) |
Given: 24x² + bx + c =(dx + e)(fx + g)
Use FOIL to expand the right side to get:
24x² + bx + c =
dfx² + gdx + efx + eg
On the left side, the coefficient of
x² is
24.
On the right side, the coefficient of
x² is
dfSo, we can conclude that:
24 = dfAt this point, the key word in the given information is that d and f are INTEGERS
Since we know that
24 = df, we can see that there aren't many pairs of INTEGER values that have a product of 24.
We get: (1)(24) = 24, (2)(12) = 24, (3)(8) = 24, and (4)(6) = 24
Quantity A = d + f
Notice that the MAXIMUM possible value of d + f occurs when the two numbers are 1 and 24, in which case we get us some of 25
This means d + f will always be less than 26
Answer: B
Cheers,
Brent