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Distinguish between polynomials by terms and degrees, using appropriate vocabulary.
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Use function notation to compute with polynomials.
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Distinguish between factoring techniques.
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Create a factored expression from a given polynomial.
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2.1: The Anatomy of a Polynomial
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Polynomials are a class of functions that are studied in calculus because they are predictable in their behavior. They are smooth, continuous curves when graphed. They are fairly easy to graph, find roots, and calculate outputs for real-number inputs. Polynomials will continue to be relevant to all of your math and science courses going forward!
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2.2: Polynomial Addition, Subtraction, Multiplication and Monomial Division
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Much of Section 2.2 is mathematics you already know, like combining like terms when adding polynomials, but we’ll keep you on your toes with the introduction of function notation! You’ll also get the added practice you crave for the various exponent properties. This section aims to strengthen your ability to work with polynomial functions using function notation.
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2.3: Review of Factoring
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Factoring is a necessary skill to have in precalculus and all math classes beyond precalculus. Factoring is a tool to simplify expressions and eases calculations. It helps us identify the roots of polynomials, making quick work of graphing without any need for computers or graphing calculators. In the same way arithmetic rules inform algebraic properties, prime factorization of real numbers informs polynomials factorization.