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Polynomials: Simplification and Factoring

Learn how to simplify and factor polynomials, find zeros, and solve quadratic equations. Explore examples and practice problems.

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Polynomials: Simplification and Factoring

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  1. Thursday, 20181206 Essential Questions • EQ11: How are polynomials simplified and factored? Word Wall Greatest Common Factor (GCF) Polynomial Monomial Binomial Trinomial Terms Agenda Bridge Math • Store your phones • Find your seat • Bellwork: Polleverywhere • Calculator • EQ11 Factoring Polynomials with leading coefficients greater than 1. • Find the zeros • Exit Ticket • Remain in seat until bell rings. Teacher Dismisses NOT the bell. It’s always a great day to be a Wolverine!

  2. Bellwork: Thursday, 20181206 • Explain what finding zeros for a quadratic equation means.

  3. EQs for 2nd QuarterRed indicates completed EQ √ • How are polynomials simplified and factored? • How do we find zeros of polynomials and graph the function? • How do we solve equations and inequalities in one variable? • How do we solve equations and inequalities in two or more variables? • How do we solve a formula for a given variable, called "solving literal equations"? • How do we create and use absolute value functions to solve problems? • How are ratios and proportions used to solve problems? • How do we factor and solve trinomials? • How do we solve systems of equations? • How do we find the distance and the midpoint between two points on coordinate plane? • How do we solve linear inequalities using multiple methods? • How do you determine relation is a function? • How do we use function notation, evaluate functions for inputs in domains? ----- √

  4. Zeros of a Polynomial Function The Zeros of a PolynomialFunction ARE the Solutions to the PolynomialEquation when the polynomial equals zero.

  5. Graph of a Polynomial Function Here is the graph of our polynomial function: The Zeros of the Polynomial are the values of x when the polynomial equals zero. In other words, the Zeros are the x-values where y equals zero.

  6. x-Intercepts of a Polynomial The points where y = 0 are called the x-intercepts of the graph. The x-intercepts for our graph are the points... and (3, 0) (-5, 0)

  7. Factoring trinomials with leading coefficient > 1 and Find Zeros. EXAMPLES Take the factors set = to 0. Solve each problem. • (x-2) = 0 (3x-14) = 0 • (5x-4) = 0 (x-2) = 0 • (4y+1) = 0 (2y-3) = 0 • (3y-1) = 0 (2y+7) = 0

  8. Factoring trinomials with leading coefficient > 1 and Find Zeros.

  9. EXIT TICKET What are the zeros of the quadratic equation? Explain.

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