Alegbra Question.. how do you evaluate a polynomial for a given value of the variable.

How do you evaluate a polynomial for a given value of the variable? Also please provide an example.

You plug the given value into the polynomial, then do the arithmetic. Here are some examples:

1. y = 2x^2 -3x + 4

a. For x = -1: y = 2(-1)^2 -3(-1) + 4 = 2 + 3 + 4 = 9

b. For x = 3: y = 2(3^2) - 3(3) + 4 = 18 - 9 + 4 = 13

2. f(x) = x^3 - 2x^2 + 1

a. f(0) = 0 - 0 + 1 = 1

b. f(2) = 2^3 - 2(2^2) + 1 = 8 - 8 + 1 = 1

c. f(a+1) = (a+1)^3 -2(a+1)^2 + 1

= (a^3 + 3a^2 + 3a + 1) - 2 (a^2 + 2a + 1) + 1

= a^3 + 3a^2 + 3a + 1 - 2a^2 - 4a - 2 + 1

= a^3 + a^2 - a

= a (a^2 + a - 1)

There you go!