**Polynomials**

Polynomial

comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

**Key Terms**

**x -4x+3**

**3xy +2y-x+18**

coefficients

This polynomial has three

terms

.

1

2

3

-constants that

are multiplied

by variables

variables

-unknown values

constants

exponents

Polynomials can NEVER be

divided by variables

2

x+2

3xy

(no negative

exponents)

Addition, Subtraction, and Multiplication

of polynomials give polynomials as

answers!

Addition / Subtraction

The

degree

of a polynomial with one variable is the

largest exponent of that

variable.

The Degree is 3 (the largest exponent of x)

4x -x-3

Examples of

Polynomials

(Yes, even "5" is a polynomial, one term is allowed, and it can even be just a constant!)

Polynomial Breakdown

When adding polynomials,

we combine "like terms," or

terms whose variables, and the

exponents of those variables, are the same.

Example: Add 2x + 6x + 5 and 3x - 2x - 1

Start with: 2x + 6x + 5 + 3x - 2x - 1

Place like terms together: 2x + 3x + 6x - 2x + 5 - 1

Add the like terms: (2+3)x + (6-2)x + (5-1)

= 5x + 4x + 4

To subtract Polynomials, first reverse the sign of each term you are subtracting (in other words turn "+" into "-", and "-" into "+"), then add as usual.

Example: Subtract 2x + 6x + 5 and 3x - 2x - 1

Start with: 2x + 6x + 5 - (3x - 2x - 1)

Switch the Signs: 2x + 6x +5 -3x + 2x + 1

Place like terms together & Add: (2-3)x + (6+2)x + (5+1)

Add as usual: (-1)x +8x + 6

Multiplication

( WARNING: This video may be boring.)

Numbers of Terms

The number of terms in a polynomial can change the way we refer to that polynomial.

Binomial- (bi- meaning "two") two terms

Monomial- (mono- meaning "one") one term

Trinomial- (tri- meaning "three") three terms

And so on...

(FOIL)

**Factoring Quadratics**

Greatest Common Factor (GCF)

Cases

Works Cited

http://www.mathsisfun.com/algebra/polynomials.htm

YouTube.com; "Teach Me How to Factor"

YouTube; Factoring Polynomial Equations - MathHelp.com - Algebra Help

Difference of Squares

+ in the back, signs will be the same

- in the back, signs will be different

Multiply the FIRST terms of each polynomial

(x-3)(x+7)

1) (x)(x)

Ex.

Multiply by the OUTSIDE terms of each polynomial

(x-3)(x+7)

2) (x)(7)

Multiply by the INSIDE terms of each polynomial

(x-3)(x+7)

3) (-3)(x)

Multiply by the LAST terms of each polynomial

(x-3)(x+7)

4) (-3)(7)

So "foiled out,"

(x-3)(x+7)= x +7x-3x-21

Combine like terms,

(x-3)(x+7)= x +7x-3x-21

(x-3)(x+7)= x + 4x -21

**2**

2

3

-2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

**Box Method**

(2x-1)(x+4)

2x

-1

x

4

2x

2

-x

8x

-4

2x

2

-x + 8x

-4

2x +7x -4

2