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 -3x4 - x3 + 20x + 3 when x = 1.
b) Find the value of -3x4 - x3 + 20x + 3 when x = -2.
Solution
a) Replace x by 1 in the polynomial:
| -3x4 - x3 + 20x + 3 |
= -3(1)4 - (1)3 + 20(1) + 3 |
| |
= -3 - 1 + 20 + 3 |
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= 19 |
So the value of the polynomial is 19 when x = 1.
b) Replace x by -2 in the polynomial:
| -3x4 - x3 + 20x + 3 |
= -3(-2)4 - (-2)3 + 20(-2) + 3
|
| |
= -3(16) - (-8) - 40 + 3 |
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= -48 + 8 - 40 + 3 |
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= -77 |
So the value of the polynomial is -77 when x = -2
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