Question

You were given polynomial f(x) = 3x^4 - 11x^3 + 7x + k and you know that f(3) = 5. Find the value of k.

Answer 1

ANSWER

k = 38

EXPLANATION

We have the polynomial:

$f(x)=3x^4-11x^3\text{ + 7x + k}$

We also have that f(3) = 5

This means that when x is 3, the function, f(x), is 5.

Therefore:

$\begin{gathered} 5=3(3)^4-11(3)^3\text{ + 7(3) + k} \\ 5\text{ = }243\text{ - }297\text{ + 21 + k} \\ 5\text{ = }-33\text{ + k} \\ \text{Collect like terms:} \\ k\text{ = 33 + 5} \\ k\text{ = 38} \end{gathered}$

That is the value of k.