A **polynomial function** is any function of the form

*P*( *x*) = *a* _{0} *x* ^{n} + *a* _{1} *x* ^{n – 1} + *a* _{2} *x* ^{n – 2} + ... + *a* _{n – 1} *x* + *a* _{n}

where the coefficients *a* _{0}, *a* _{1}, *a* _{2}, ..., *a* _{n} are real numbers and *n* is a whole number. Polynomial functions are evaluated by replacing the variable with a value. The instruction “evaluate the polynomial function *P*( *x*) when *x* is replaced with 4” is written as “find *P*(4).”

##### Example 1

If *P*( *x*) = 3 *x* ^{3} – 2 *x* ^{2} + 5 *x* + 3, find *P*(–4).

##### Example 2

If *f* ( *x*) = 3 *x* ^{2} – 4 *x* + 5, find *f* ( *x* + *h*).