Exponents and Polynomials

Exponents and Polynomials

January 11, 2021

Monomials

A monomial is a constant, variable, or product of numbers and variables.
Examples:  $-6$  ,  $7x$  ,  $\frac{1}{2}x^2y$   

EXPONENT RULES REVIEW

• Product Rule:  $x^a\cdot x^b=x^{a+b}$       example:   $x^3\cdot x^7=x^{3+7}=x^{10}$   

• Power Rule:   $\left(x^a\right)^b=x^{ab}$      example:   $\left(y^6\right)^2=y^{6\cdot2}=y^{12}$    

• Quotient Rule:   $\frac{x^a}{x^b}=x^{a-b}$      example:   $\frac{b^5}{b^3}=b^{5-3}=b^2$  

• Negative Exponent Rule:   $x^{-a}=\frac{1}{x^a}$     example:   $p^{-2}=\frac{1}{p^2}$  

• Zero Exponent Rule:   $x^0=1\ \left(x\ne0\right)$     example:   $\left(4x^3\right)^0=1$  

When ADDING OR SUBTRACTING monomials, COMBINE LIKE TERMS

Example:   $2x^4+3x^4=5x^4$  

Polynomials

The sum or difference of many monomials.

The highest exponent in the polynomials is the degree

Standard Form: Exponents are in descending order

Classifying Polynomials by Degree

• Exponent of 0 - Constant

• Exponent of 1 - Linear

• Exponent of 2 - Quadratic

• Exponent of 3 - Cubic

• Exponent of 4 - Quartic

• Exponent of 5 - Quintic

Classifying Polynomials by Number of Terms

• 1 Term: Monomial

• 2 Terms: Binomial

• 3 Terms: Trinomial

• 4+ Terms: Polynomial