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

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) (Show Source): You can put this solution on YOUR website!

Now we can extract some facts:
Fact 1: Because the leading coefficients must be equal
Fact 2: Because the first degree term coefficients must be equal
Fact 3: Because the constant coefficients must be equal

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

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

Check:
Does ?

, Check!

Hope this helps.
Answer by jpa65@hotmail.com(9) (Show Source): You can put this solution on YOUR website!

RELATED QUESTIONS
{{{(3x)/(2x+5)-(5x+2)/(2x-5)=(Ax^2+Bx+C)/((2x+5)(2x-5))}}} Find the smallest values of (answered by ankor@dixie-net.com)
Identify the values of a, b, and c you would substitute into the quadratic formula to... (answered by lefty4ever26)
Given that (x^2-ax+2)(x-b)=x^3-7x^2+14x+c, find the possible values of the constant a,b... (answered by Fombitz)
Find the sum of a, b, c, and d if (x^3 - 2x^2 + 3x + 5)/(x + 2) = ax^2 + bx + c +... (answered by josgarithmetic,timofer)
if ax^2+bx+c=0 and x=2 or 6/7 what are the values of a b... (answered by ikleyn)
find the values of a,b and c of teh quadration y=ax^2+bx+c if it passes through the... (answered by tommyt3rd)
If a and b; are roots of the equation {{{ ax ^ 2 + bx + c = 0 }}} , find the values of: (answered by ikleyn)
Find the values a,b,c of the quadratic y=ax^2+bx+c if it passes through the points... (answered by stanbon)
Given the identity Ax^3+x^2-2x-3=(3x+B)(x-1)(x+2)+C(x-1)+D , find the values of the... (answered by MathTherapy)