Question

If f(x) = 3x^3 + Ax^2 + 8x - 9 and f(2)= 7, what is the value of A?

Answer 1

f(2) = 7 means plugging in "2" into x (of the equation) and it will give us "7" as the answer.

Let's do this:

`\begin{gathered} f(x)=3x^3+Ax^2+8x-9 \\ f(2)=7 \\ 3(2)^3+A(2)^2+8(2)-9=7 \end{gathered}`

Now, we simply do algebra:

`\begin{gathered} 3(2)^3+A(2)^2+8(2)-9=7 \\ 3(8)+A(4)+16-9=7 \\ 24+4A+16-9=7 \\ 4A+31=7 \\ 4A=7-31 \\ 4A=-24 \\ A=-(24)/(4) \\ A=-6 \end{gathered}`