SOLUTION: If (ax+b)(2x-3)=18x^2-23x+c, find the values of a, b, and c.

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Question 112542: If (ax+b)(2x-3)=18x^2-23x+c, find the values of a, b, and c.
Found 2 solutions by solver91311, jpa65@hotmail.com:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28ax%2Bb%29%282x-3%29=18x%5E2-23x%2Bc

2ax%5E2-3ax%2B2bx-3b=18x%5E2-23x%2Bc
2ax%5E2%2B%28-3a%2B2b%29x-3b=18x%5E2-23x%2Bc

Now we can extract some facts:
Fact 1: 2a=18 Because the leading coefficients must be equal
Fact 2: -3a%2B2b=-23 Because the first degree term coefficients must be equal
Fact 3: -3b=c Because the constant coefficients must be equal

Solving the Fact 1 equation for a gives us a=9. We can use this value to solve the Fact 2 equation, thus:

-3%289%29%2B2b=-23
2b=-23%2B27
2b=4
b=2

And then using our newly found value for b, we can solve the last equation:

-3%282%29=c
c=-6

Check:
Does %289x%2B2%29%282x-3%29=18x%5E2-23x-6?

%289x%2B2%29%282x-3%29
18x%5E2-27x%2B4x-6
18x%5E2-23x-6, Check!

Hope this helps.

Answer by jpa65@hotmail.com(9) About Me  (Show Source):