Characteristics
Evaluating
Because polynomials fit the definition of a function, [for every input (x-value) there is exactly one output (y-value)] function notation can be used. Instead of writing y = x4 + 6x3 - x + 2, in function notation it would be written P(x) = x4 + 6x3 - x + 2. The letter, P, is often used for polynomial functions.
Evaluating a polynomial is the same as evaluating linear or quadratic functions: substitute the given value of x, and find the value for y.
Example Evaluate P(x) = 2x3 - x2 - 4x + 2, when x = -3.
Step 1. Substitute "-3" for the "x", remembering to be careful with parentheses and the negatives:
P (-3) = 2(-3)3 - (-3)2 - 4(-3) + 2
Step 2. Simplify the expression.
2(-27) - (9) + 12 + 2
-54 - 9 + 14
-63 + 14
-49
P (-3) = -49