## Evaluating a Polynomial For a Given Value

We have already learned how to evaluate expressions. Since polynomials are expressions, we’ll follow the same procedures to evaluate a **polynomial**. We will substitute the given value for the variable and then simplify using the order of operations.

## Example

Evaluate \(5{x}^{2}-8x+4\) when

- \(x=4\)
- \(x=-2\)
- \(x=0\)

### Solution

\(x=4\) | |

Simplify the exponents. | |

Multiply. | |

Simplify. |

\(x=-2\) | |

Simplify the exponents. | |

Multiply. | |

Simplify. |

\(x=0\) | |

Simplify the exponents. | |

Multiply. | |

Simplify. |

## Example

The polynomial \(-16{t}^{2}+250\) gives the height of a ball \(t\) seconds after it is dropped from a 250 foot tall building. Find the height after \(t=2\) seconds.

### Solution

\(\begin{array}{cccc}& & & \phantom{\rule{4em}{0ex}}-16{t}^{2}+250\hfill \\ \text{Substitute}\phantom{\rule{0.2em}{0ex}}t=2.\hfill & & & \phantom{\rule{4em}{0ex}}-16{\left(2\right)}^{2}+250\hfill \\ \text{Simplify.}\hfill & & & \phantom{\rule{4em}{0ex}}-16·4+250\hfill \\ \text{Simplify.}\hfill & & & \phantom{\rule{4em}{0ex}}-64+250\hfill \\ \text{Simplify.}\hfill & & & \phantom{\rule{4em}{0ex}}186\hfill \\ & & & \phantom{\rule{4em}{0ex}}\text{After 2 seconds the height of the ball is 186 feet.}\hfill \end{array}\)

## Example

The polynomial \(6{x}^{2}+15xy\) gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side *x* feet and sides of height *y* feet. Find the cost of producing a box with \(x=4\) feet and \(y=6\) feet.

### Solution

Simplify. | |

Simplify. | |

Simplify. | |

The cost of producing the box is $456. |

Thanks for this tutorial

Please guys help me with polynomials of graph