Let $f(x)=2x^4+x^3+x^2-3x+r$. For what value of $r$ is $f(2)=0$?

For what value of r in the formula:  f(x)  =  2x⁴ + x³ + x²- 3x + r  does  f(2)  =  0?

 

Replace x with 2:  2·2⁴ + 2³ + 2²- 3·2 + r  =  32 + 8 + 4 - 6 + r  =  38 + r

This value is to equal 0:   38 + r  =  0

                                                 r  =  -38