Evaluating Polynomials
A polynomial is an algebraic expression. Like other algebraic expressions
involving variables, a polynomial has no specific value unless the variables are
replaced by numbers. A polynomial can be evaluated without using funcion
notation.
Value of a Polynomial
a) Find the value of 3x^{4}  x^{3} + 20x + 3 when x = 1.
b) Find the value of 3x^{4}  x^{3} + 20x + 3 when x = 2.
Solution
a) Replace x by 1 in the polynomial:
3x^{4}  x^{3} + 20x + 3 
= 3(1)^{4}  (1)^{3} + 20(1) + 3 

= 3  1 + 20 + 3 

= 19 
So the value of the polynomial is 19 when x = 1.
b) Replace x by 2 in the polynomial:
3x^{4}  x^{3} + 20x + 3 
= 3(2)^{4}  (2)^{3} + 20(2) + 3


= 3(16)  (8)  40 + 3 

= 48 + 8  40 + 3 

= 77 
So the value of the polynomial is 77 when x = 2
