'Leading coefficient' presentation slideshows

5.1 Polynomial Functions

In this section, we will study the following topics: Identifying polynomial functions and their degree Determining end behavior of polynomial graphs Finding real zeros of polynomial functions and their multiplicity Analyzing the graph of a polynomial function. 5.1 Polynomial Functions.

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Polynomial functions

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Warm Up

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GPS Algebra

GPS Algebra. EQ: How do we add and subtract polynomials? Standard: M.ALGI.4.22: Polynomials: Determine/Coefficient M.ALGI.4.13: Polynomials: Add/Subtract. Mono mial 2 Bi nomial 3 Tri nomial 4+ Polynomial . 0 Constant 1 Linear 2 Quadratic

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FACTORING

FACTORING. Factoring means to write an expression as a product of primes. To check your answer to a factoring problem you simplify it by multiplying out the factors.

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Chapter 2: Polynomial, Power, and Rational Functions

Section 2-4: Real Zeros of Polynomial Functions. Chapter 2: Polynomial, Power, and Rational Functions. Objectives. You will learn about: Long division and the division algorithm Remainder and factor theorems Synthetic division Rational zeros theorem Upper and lower bounds Why?

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Warm Up

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Identify, evaluate, add, and subtract polynomials. Classify and graph polynomials.

Objectives. Identify, evaluate, add, and subtract polynomials. Classify and graph polynomials. Vocabulary. monomial polynomial degree of a monomial degree of a polynomial leading coefficient binomial trinomial polynomial function. a 7. 8. 1. 1. 5 y 2. 2. 2.

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Warm Up Identify all the real roots of each equation.

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POLYNOMIALS REVIEW

The DEGREE of a polynomial is the largest degree of any single term in the polynomial (Polynomials are often written in descending order of the degree of its terms) COEFFICIENTS are the numerical value of each term in the polynomial

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3-1

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3.4 Zeros of Polynomial Functions

3.4 Zeros of Polynomial Functions. The Fundamental Theorem of Algebra. If f(x) is a polynomial of degree n , where n>0, then f has at least one zero in the complex number system. Linear Factorization Theorem.

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3.4 Zeros of Polynomial Functions

3.4 Zeros of Polynomial Functions. The Fundamental Theorem of Algebra. If f(x) is a polynomial of degree n , where n>0, then f has at least one zero in the complex number system. Linear Factorization Theorem.

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Polynomial Functions and Their Graphs

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9.2 Notes

9.2 Notes . Solving Quadratic Equations by Finding Square Roots. Warm-up. 1) 2) 3). Objective:. solve a quadratic equation by finding square roots Key terms: - quadratic equation - leading coefficient. Solve Quadratic Equations. A quadratic equation in standard form looks like this:

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Sum and Product Roots

Sum and Product Roots. Lesson 6-5. The Sum and the Product Roots Theorem. In a quadratic whose leading coefficient is 1: the sum of the roots is the negative of the coefficient of x; the product of the roots is the constant term. Sum and Product of Roots.

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Choosing a Factoring Method

Choosing a Factoring Method. To decide on a factoring method for a second-degree equation, look at the number of terms: If a polynomial has 2 terms, (binomial) A. Check whether the second term is a perfect square. If it is the difference of squares:

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