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Bellwork

Bellwork. Bellwork Solution. Add and Subtract Polynomials. Section 9.1. The Concept. In Chapter 3 we talked about simplifying expressions based upon like terms However those like terms were limited to first-order polynomials

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Bellwork

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  1. Bellwork

  2. Bellwork Solution

  3. Add and Subtract Polynomials Section 9.1

  4. The Concept • In Chapter 3 we talked about simplifying expressions based upon like terms • However those like terms were limited to first-order polynomials • Today we’re going to talk about the naming scheme of polynomials and also how we can utilize an understanding of like terms to simplify them

  5. Definitions • In order to understand polynomials, we must first understand what is a monomial • Simply put a monomial is a single term comprised of a coefficient, variable and whole number exponent • The degree of a monomial is the sum of the magnitudes of the exponents contained within • For instance Degree (sum of exponents) 0 1 2 1+2=3

  6. Definitions • A string of monomials attached by addition or subtraction is called a polynomial • The degree (or order) of a polynomial is the highest degree contained within • The correct procedure for writing polynomials is to write the terms in decreasing degree • For example Degree 2 1 2+2=4 1+2=3

  7. Sticky Points • In order for a string of terms to be considered a polynomial, there can be no non-monomial components • This means that no terms have negative or variable exponents • As well, the leading coefficient of a polynomial is the coefficient attached to the highest degree term • The leading coefficient is important because it indicates the magnitude and direction of the graph when x is very large

  8. WHY? • Polynomials have many properties, all of which are based upon the fact that they fall within a certain set of guidelines • Polynomials also model many real life situations • If the criteria are not met, the ramifications indicate a shift in our ability to utilize that criteria…

  9. Adding and Subtracting • Much like adding and subtracting first order polynomials, when we add and subtract polynomials we do it by like terms • However these like terms are grouped by the degree of each term and kind of variable • Subtracting polynomials is the similar, but we have to first distribute our negative sign • Let’s do some examples

  10. Examples • Simplify

  11. Examples • Simplify

  12. Examples • Simplify

  13. Examples • Simplify

  14. Homework • 9.1 • 1-10, 17-28, 32, 34, 38

  15. Practical Example • During the period of 1995-2005, the number of hours an individual person watched broadcast television B and cable and satellite television C can be modeled by: where t is the number of years since 1999. About how many hours did people watch television in 2002?

  16. Most Important Points • A monomial cannot have a variable, negative or fractional exponent • The degree of a monomial is the sum of its exponents • The degree of a polynomial is the highest degree monomial contained within • Adding & Subtracting polynomials is done on the basis of like terms

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