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Transcript of Polynomials
comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"
This polynomial has three
Polynomials can NEVER be
divided by variables
Addition, Subtraction, and Multiplication
of polynomials give polynomials as
Addition / Subtraction
of a polynomial with one variable is the
largest exponent of that
The Degree is 3 (the largest exponent of x)
(Yes, even "5" is a polynomial, one term is allowed, and it can even be just a constant!)
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
( 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...
Greatest Common Factor (GCF)
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
Multiply by the OUTSIDE terms of each polynomial
Multiply by the INSIDE terms of each polynomial
Multiply by the LAST terms of each polynomial
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
-x + 8x
2x +7x -4