If (x+7)(x-2) = ax^2 + bx + c for all values of x, where a, b, and c are constants, what is the value of a + b - c

Question

amoodarya · Answer

expand (x+7)(x-2)
then compare rhs ,lhs

usukidoll · Answer

that's what I was thinking too... if we use the FOIL method to expand (x+7)(x-2) we can figure out what a, b, and c is

amoodarya · Answer

$$(x+7)(x-2)=x^2+5x-14=ax^2+bx+c\ax^2=x^2\bx=5x\c=-14$$

amoodarya · Answer

another method is : 
put for example x=0,1,2  both side 
then you have a system of equation to find a,b,c

anonymous · Answer

ohhh okay! It makes much more sense now! Thanks guys!! :)

usukidoll · Answer

it looked like a simple proof problem where we start from the left side and have it equal to the right side, so by expanding (x+7)(x-2) using FOIL we will have $$x^2+5x-14 $$. Then we compare that equation to $$ax^2+bx+c $$ which is the standard quadratic equation.

anonymous · Answer

Got it! Thank you!