PolynomialsPolynomialsEQ – 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, 7Non Examples: p2.4, 2x, ,

x 2

5

g

Polynomial – one monomial or the sum or difference of monomials

Examples: , , , x+4Non-Examples: , ,

74

3

1yx

22 42 yx

22 ba 3.010xy

432 yx

yx33

• Polynomials are classified by their number of terms

One term – monomialTwo terms – binomialThree terms – trinomialFour or more-polynomial

• Polynomials are also classified by degrees.

• The degree of a polynomial is the same as the term with the greatest degree

524 52 xyxx Degree 2 Degree 5 Degree 1 Degree 0

This polynomial has a degree of 5

Degrees of a Polynomial

• O - constant• 1st – linear• 2nd-Quadratic• 3rd-Cubic• 4th-Quartic

• Leading coefficient is in front of the highest degree term.

• A constant can be a leading coefficient if by itself.• 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