SOLUTION: If (ax-3)(bx+6)=24x^2+cx-18 for all values of x and a+b=10, what are two possible values for c? A. 2 and 12 B. 6 and 24 C. 10 and 30 D. 16 and 30

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If (ax-3)(bx+6)=24x^2+cx-18 for all values of x and a+b=10, what are two possible values for c? A. 2 and 12 B. 6 and 24 C. 10 and 30 D. 16 and 30      Log On


   

Question 1040243: If (ax-3)(bx+6)=24x^2+cx-18 for all values of x and a+b=10, what are two possible values for c?
A. 2 and 12
B. 6 and 24
C. 10 and 30
D. 16 and 30
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%28ax-3%29%28bx%2B6%29=24x%5E2%2Bcx-18
abx%5E2-3bx%2B6ax-18=24x%5E2%2Bcx-18
abx%5E2%2B%286a-3b%29x-18=24x%5E2%2Bcx-18
-
system%28ab=24%2C6a-3b=c%29 and given a%2Bb=10.

Question is, what can be c?
Observe, three equations and three unknown variables.
system%28ab=24%2C6a-3b=c%2Ca%2Bb=10%29.

TWO of the equations are only in the two unknowns a and b.
b=10-a
-
a%2810-a%29=24
10a-a%5E2=24
-a%5E2%2B10a-24=0
a%5E2-10a%2B24=0
%28a-4%29%28a-6%29=0
-
Possible, system%28a=4%2Cor%2Ca=6%29
Correspondingly, system%28b=6%2Cor%2Cb=4%29

Possible c values:
c=6a-3b as already found,
c=6%2A4-3%2A6=highlight%286%29
or
c=6%2A6-3%2A4=36-12=highlight%2824%29