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Polynomials

A brief description of important concepts of polynomials, plus adding, subtracting, and multiplying; including YouTube video.
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on 3 April 2016

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Transcript of Polynomials

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
Full transcript