When dealing with differing kinds of Polynomials, there are several varieties. Today we will explore a few different variations, and break down the simple formula for naming them. A monomial is the product of non-negative powers of variables. A monomial has no variables in its denominator and will only have one term.
A trinomial is the sum of three monomials, meaning it will be the sum of three unlike terms. A good clue when trying to remember the meaning of these terms is the prefix on each word. Polynomials are in simplest form when they contain no similar terms.
Similar terms are terms in the polynomial which are raised to the same power. Evaluate a Polynomial for a Given Value. In the following exercises, evaluate each polynomial for the given value. Evaluate when:. A painter drops a brush from a platform 75 feet high. The polynomial gives the height of the brush seconds after it was dropped. A girl drops a ball off a cliff into the ocean. The polynomial gives the height of a ball seconds after it is dropped from a foot tall cliff.
A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial Find the revenue received when dollars. A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial Find the revenue received when dollars.
Fuel Efficiency The fuel efficiency in miles per gallon of a car going at a speed of miles per hour is given by the polynomial. Find the fuel efficiency when. Stopping Distance The number of feet it takes for a car traveling at miles per hour to stop on dry, level concrete is given by the polynomial. Find the stopping distance when. Rental Cost The cost to rent a rug cleaner for days is given by the polynomial. Find the cost to rent the cleaner for 6 days.
Height of Projectile The height in feet of an object projected upward is given by the polynomial where represents time in seconds. Temperature Conversion The temperature in degrees Fahrenheit is given by the polynomial where represents the temperature in degrees Celsius.
Find the temperature in degrees Fahrenheit when. Using your own words, explain the difference between a monomial, a binomial, and a trinomial. Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5. Ariana thinks the sum is. What is wrong with her reasoning? Jonathan thinks that and are both monomials. What is wrong with his reasoning? You have achieved the objectives in this section.
Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific. This must be addressed quickly because topics you do not master become potholes in your road to success.
In math every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved? This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed.
The degree of a polynomial is the highest degree of all its terms. Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in standard form. Look back at the polynomials in the previous example. Notice that they are all written in standard form. Get in the habit of writing the term with the highest degree first.
Skip to main content.
0コメント