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Published byFay Shields Modified over 8 years ago

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**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?

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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, ,

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**Polynomial – one monomial or the sum or difference of monomials**

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

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**Polynomials are classified by their number of terms**

One term – monomial Two terms – binomial Three terms – trinomial Four or more-polynomial

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**Polynomials are also classified by degrees.**

The degree of a polynomial is the same as the term with the greatest degree Degree Degree Degree Degree 0 This polynomial has a degree of 5

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**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.

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**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.

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Combining like terms

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Try these:

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**Using the Distributive Property**

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Try these:

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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

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**To add them vertically:**

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Try these:

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**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

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Finding the opposite

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To Subtract:

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Try these:

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**Multiplying polynomials by monomials**

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**Or you may need the distributive property**

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Try these:

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**Multiplying binomials**

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

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**Check out these examples:**

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Try these:

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**Factoring Polynomials**

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

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

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**Leading coefficient not 1**

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Special factoring Patterns in factoring…

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Try these:

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The End

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