Adding and Subtracting Polynomials © Michael Swaner

Notes A monomial is an expression that is a number, a variable, or a product of a number and one or more variables. Really it boils down to an expression that stands alone as one term Ex. 12 x

Notes A Binomial is the sum or difference of two monomials. Really it boils down to having two terms. Ex.

Notes As you can probably guess, a trinomial is the sum or difference of ______________ monomials Any sum or difference with more than 3 terms is simply called a polynomial 3

Notes The degree of a monomial is the sum of the exponents x = degree of 1 = degree of 1 = degree of 3 = degree of 27

Notes Standard form of a polynomial is when the degrees decrease from left to right. 5 4 3 2 1 0

Notes When classifying polynomials, you must put the polynomials in standard form. linear quadratic cubic

Notes Any polynomial with a degree larger than 3 is named by its highest degree: 5th degree polynomial 6th degree polynomial 15th degree polynomial

Adding Polynomials-horizontally When adding polynomials horizontally, combine like terms.

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Subtracting Polynomials-Horizontally When subtracting polynomials horizontally you must first distribute the negative to all terms

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Adding Polynomials-Vertically Line up like terms by “place value”

What if a Place Value is Missing? All that means is

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Subtracting Polynomials-Vertically Line up like terms by “place value”

Try

Closure decrease highest degree What is the degree? Standard form of a polynomial is when the degrees _____________ from left to right. Any polynomial with a degree larger than 3 is named by its ______ _______ decrease highest degree

Closure combine negative all When adding or subtracting polynomials horizontally ___________ like terms. When subtracting polynomials horizontally you must distribute the ___________ to _________ terms. combine negative all

Closure When adding or subtracting polynomials vertically, __________ __________ like terms. If a place value is missing, it really means ___________ line up zero