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Study Guides > Prealgebra

Evaluating a Polynomial for a Given Value

Learning Outcomes

  • Evaluate a polynomial for integer values
  In The Language of Algebra we evaluated expressions. 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]
 

try it

[ohm_question]146086[/ohm_question]
The following video provides another example of how to evaluate a quadratic polynomial for a negative number. https://youtu.be/c7XkBD0fszc

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.

Answer: Solution

[latex]-16t^2+300[/latex]
Substitute [latex]3[/latex] for [latex]t[/latex] [latex]-16(\color{red}{3})^2+300[/latex]
Simplify the expression with the exponent. [latex]-16\cdot{9}+300[/latex]
Multiply. [latex]-144+300[/latex]
Simplify. [latex]156[/latex]

 

try it

[ohm_question]146088[/ohm_question]  
 

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