Evaluating a Polynomial for a Given Value

Learning Outcomes

  • Evaluate a polynomial for integer values

Previously we evaluated expressions by “plugging in” numbers for variables. Since polynomials are expressions, we’ll follow the same procedures to evaluate polynomials—substitute the given value for the variable into the polynomial, and then simplify.

example

Evaluate [latex]3{x}^{2}-9x+7[/latex] when

1. [latex]x=3[/latex]
2. [latex]x=-1[/latex]

Solution

1. [latex]x=3[/latex]
[latex]3{x}^{2}-9x+7[/latex]
Substitute [latex]3[/latex] for [latex]x[/latex] [latex]3{\left(3\right)}^{2}-9\left(3\right)+7[/latex]
Simplify the expression with the exponent. [latex]3\cdot 9 - 9\left(3\right)+7[/latex]
Multiply. [latex]27 - 27+7[/latex]
Simplify. [latex]7[/latex]
2. [latex]x=-1[/latex]
[latex]3{x}^{2}-9x+7[/latex]
Substitute [latex]−1[/latex] for [latex]x[/latex] [latex]3{\left(-1\right)}^{2}-9\left(-1\right)+7[/latex]
Simplify the expression with the exponent. [latex]3\cdot 1 - 9\left(-1\right)+7[/latex]
Multiply. [latex]3+9+7[/latex]
Simplify. [latex]19[/latex]

 

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The following video provides another example of how to evaluate a quadratic polynomial for a negative number.

example

The polynomial [latex]-16{t}^{2}+300[/latex] gives the height of an object [latex]t[/latex] seconds after it is dropped from a [latex]300[/latex] foot tall bridge. Find the height after [latex]t=3[/latex] seconds.

 

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