Exponents and Polynomials

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Presentation transcript:

Exponents and Polynomials Opening Routine

Exponents and Polynomials Opening Routine

Topic VII: Exponents and Polynomials

Exponents and Polynomials Objective: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Essential Question: How combining like terms help us when adding and subtracting polynomials?

Exponents and Polynomials Vocabulary Monomial: Is an algebraic expression consisting of a single term (although that term could be an exponent). Binomial: Is a polynomial algebraic expression or equation with just two terms. Trinomial: Is a polynomial algebraic expression or equation with three terms. Polynomial: Is an algebraic expression or equation with more than one term, constructed from variables and constants using only the operations of addition, subtraction, multiplication and non-negative whole- number exponents.

Exponents and Polynomials Vocabulary Constant term: Is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables. Coefficient: Is the factor of the term (i.e. the number in front of the letter) in a mathematical expression or equation. Like-Terms: Are terms that contain the same variables raised to the same power. Like terms can be combined to shorten and simplify algebraic expressions.

Exponents and Polynomials Vocabulary Leading Coefficient: Is the coefficient of the term of highest degree in a given polynomial. Degree of a monomial: Is the sum of the exponents of the variables that appear in it. Degree of a polynomial: The degree of a polynomial is the highest degree of its terms when the polynomial is expressed in a linear combination of monomials.

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials

Exponents and Polynomials Adding and Subtracting Polynomials Guided Practice – WE DO What is the simpler form of (4m3  m + 9)  (4m2 + m  12)? 4m3  m + 9  4m2  m + 12 Write the opposite of each term in the polynomial being subtracted 4m3  4m2 ( m  m) + (9 + 12) Group like terms 4m3  4m2  2m + 21 Simplify

Exponents and Polynomials Adding and Subtracting Polynomials Independent Practice - YOU DO Adding and Subtracting Polynomials Worksheet Exercises 1 – 24

Exponents and Polynomials Adding and Subtracting Polynomials Closure Essential Question: How combining like terms help us when adding and subtracting polynomials?