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Studienführer > 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 3x2−9x+73{x}^{2}-9x+7 when 1. x=3x=3 2. x=−1x=-1 Solution
1. x=3x=3
3x2−9x+73{x}^{2}-9x+7
Substitute 33 for xx 3(3)2−9(3)+73{\left(3\right)}^{2}-9\left(3\right)+7
Simplify the expression with the exponent. 3⋅9−9(3)+73\cdot 9 - 9\left(3\right)+7
Multiply. 27−27+727 - 27+7
Simplify. 77
2. x=−1x=-1
3x2−9x+73{x}^{2}-9x+7
Substitute −1−1 for xx 3(−1)2−9(−1)+73{\left(-1\right)}^{2}-9\left(-1\right)+7
Simplify the expression with the exponent. 3⋅1−9(−1)+73\cdot 1 - 9\left(-1\right)+7
Multiply. 3+9+73+9+7
Simplify. 1919
 

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 −16t2+300-16{t}^{2}+300 gives the height of an object tt seconds after it is dropped from a 300300 foot tall bridge. Find the height after t=3t=3 seconds.

Answer: Solution

−16t2+300-16t^2+300
Substitute 33 for tt −16(3)2+300-16(\color{red}{3})^2+300
Simplify the expression with the exponent. −16⋅9+300-16\cdot{9}+300
Multiply. −144+300-144+300
Simplify. 156156

 

try it

[ohm_question]146088[/ohm_question]  
 

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