PE - What is a Polynomial? Lesson

What is a Polynomial?

A polynomial looks like this:

From the first page, you'll remember that this polynomial has 3 terms. Polynomial means "many terms".

A polynomial can have:

• Exponents (only whole number exponents)
• Variables (usually x and y)                      
• Constants (like -1 in the polynomial above)

A polynomial cannot have:

• Division by variables: $\frac{1}{x+2}$ is not a polynomial!
• Negative exponents
• Fraction exponents 

You will study polynomials for the next few years in various algebra courses. Mathematicians like to work with polynomials because they are strictly defined and can model various situations! We can also perform operations with them!

"Is this a Polynomial?" Practice

1. $\frac{2}{3}xy^4-7x^2$
   
2. $\frac{3}{x}+x^2$
3. $3x^{-3}+x^{-2}$
4. $\frac{x}{4}+\frac{x^2}{8}$
5. $3^x+2$
6. $7x$

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

 

The degree of a term is found by adding the exponents. The degree of a polynomial is the highest degree out of each term.

Polynomials are written in standard form when they are written in order of degree from greatest to least. So the polynomial above is written in standard form when it is written as:

$3y^5+2xy^3-8x^2y$

Degree and Standard Form Practice

 

What is the degree of the polynomial? Practice

1. $3x^2y^5$
2. $2x^3y^2+y^3-5x^2$
3. $x^2+2x-5$
4. $2x-7$
5. $5$

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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