EQ – what is a polynomial, and how can I tell if a term is one? Polynomials Polynomials EQ – what is a polynomial, and how can I tell if a term is one?

Terms: Monomial – a number or product of numbers and variables with exponents that are whole numbers Examples: 2n, x3, 4a5b6, 7 Non Examples: p2.4, 2x, ,

Polynomial – one monomial or the sum or difference of monomials Examples: , , , x+4 Non-Examples: , ,

Polynomials are classified by their number of terms One term – monomial Two terms – binomial Three terms – trinomial Four or more-polynomial

Polynomials are also classified by degrees. The degree of a polynomial is the same as the term with the greatest degree Degree 2 Degree 5 Degree 1 Degree 0 This polynomial has a degree of 5

Degrees of a Polynomial Leading coefficient is in front of the highest degree term. A constant can be a leading coefficient if by itself. O - constant 1st – linear 2nd-Quadratic 3rd-Cubic 4th-Quartic Standard form –polynomial in descending order of degrees.

Simplifying Polynomials You can simplify a polynomial by adding or subtracting like terms ( they must have the same variable and the same degree) Or you can simplify one using the distributive property Leading coefficient - coefficient in front of the term with highest degree.

Combining like terms

Try these:

Using the Distributive Property

Try these:

Adding Polynomials To add two polynomials, you can combine like terms or line up the like terms and add them vertically. Horizontal format Vertical format

To add them vertically:

Try these:

Subtracting Polynomials This is like adding the opposite -- find the opposite of the second number and then add like you did before Horizontal format Vertical format

Finding the opposite

To Subtract:

Try these:

Multiplying polynomials by monomials

Or you may need the distributive property

Try these:

Multiplying binomials Think FOIL (first, outside, inside, and last) This is the order you will multiply them!

Check out these examples:

Try these:

Factoring Polynomials Factoring is dividing out factors that are the same in the polynomial Factoring binomials are reversing FOIL.

Factoring Taking out the GCF of the terms of a polynomial.

Leading coefficient not 1

Special factoring Patterns in factoring…

Try these:

The End