cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Domain: Arithmetic with Polynomials and Enduring Understanding(s): Use the following Lesson(s) to introduce Vocabulary Rational Expressions conceptual understanding. Polynomials can be divided using steps Synthetic division, remainder theorem that are similar to long division steps that Cluster: Understand the relationship are used to divide whole numbers. between zeros and factors of Polynomials Writing in Math How does dividing a polynomial by a binomial Essential Question(s): Know and the Remainder Theorem: For a determine if that binomial is a factor of the polynomial p(x) and a number a, the remainder When is it best to use long division vs. synthetic polynomial? on division by x a is p(a), so p(a) = 0 if and division? – only if (x a) is a factor of p(x). – Have students to write a sentence(s) and Objective(s): create and solve an example and Domain: Arithmetic with Polynomials and counterexample about their thinking. Use the textbook resources to address Students will divide polynomials by long Rational Expressions procedural skill and fluency. division. Students will divide polynomials by Pearson Graphic Organizer Cluster: Understand the relationship between synthetic division. 5-4 Dividing Polynomials zeros and factors of Polynomials Glencoe 6.2 Dividing Polynomials Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form Lesson Videos q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using . inspection, long division, or, for the more complicated examples, a computer algebra system. Use the following Lesson(s) to introduce Enduring Understanding(s): Vocabulary concepts/build conceptual understanding. (x-a) is a factor of a polynomial if and only if Rational Root Theorem, Conjugate Root a is a root of the related polynomial Theorem, Descartes’ Rule of Signs equation.
cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Domain: Arithmetic with Polynomials and Rational Expressions Cluster: Understand the relationship between zeros and factors of Polynomials Know and the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). Domain: Arithmetic with Polynomials and Rational Expressions Cluster: Understand the relationship between zeros and factors of Polynomials Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Enduring Understanding(s): Polynomials can be divided using steps that are similar to long division steps that are used to divide whole numbers. Essential Question(s): When is it best to use long division vs. synthetic division? Objective(s): Students will divide polynomials by long division. Students will divide polynomials by synthetic division. Use the following Lesson(s) to introduce conceptual understanding. Use the textbook resources to address procedural skill and fluency. Pearson 5-4 Dividing Polynomials Glencoe 6.2 Dividing Polynomials Lesson Videos . Vocabulary Synthetic division, remainder theorem Writing in Math How does dividing a polynomial by a binomial determine if that binomial is a factor of the polynomial? Have students to write a sentence(s) and create and solve an example and counterexample about their thinking. Graphic Organizer Enduring Understanding(s): (x-a) is a factor of a polynomial if and only if a is a root of the related polynomial equation. Use the following Lesson(s) to introduce concepts/build conceptual understanding. Vocabulary Rational Root Theorem, Conjugate Root Theorem, Descartes’ Rule of Signs