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## Algebraic Expressions

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**Algebraic Expressions**Factoring and Simplifying (1.3)**POD– send answers via Navigator**True or false? What’s your reasoning? (a ÷ b) ÷ c = a ÷ (b ÷ c)**SAT Question #1**Send your responses via Navigator. If then P = How did you get your answer?**SAT Question #2**Send your responses via Navigator. If find 6x. How did you get your answer?**SAT Question #3**Send your responses via Navigator. Simplify How did you get your answer?**Polynomials– The RULE: expressions with numbers and**variables involving only addition, subtraction, and multiplication Following this rule, all exponents will be non-negative integers. We’re also assuming here that we combine all like terms. anxn + an-1xn-1+ an-2xn-2 + an-3xn-3 + … a1x + a0 Let’s start by reviewing the pieces. Some vocabulary: coefficient, leading coefficient variable degree monomial, binomial, trinomial linear, quadratic, cubic, etc. Is 5 a polynomial? Give an example of a polynomial and a non-polynomial.**Multiplying**Multiply these: (2x + 3)(2x – 3) (2x + 3)2**Factoring– the opposite of multiplying**What’s the first rule in factoring? Try these. You can verify your answers with CAS. x2 + x - 6 6x2 - 7x - 3 12x3 - 36x2y + 27xy2 a3 + b3 a3 - b3**Factoring– the opposite of multiplying**What’s the first rule in factoring? Try these. You can verify your answers with CAS. x2 + x – 6 = (x + 3)(x – 2) 6x2 - 7x – 3 = (2x – 3)(3x + 1) 12x3 - 36x2y + 27xy2 = 3x(4x2 – 12xy + 9y2) = 3x(2x – 3)2 a3 + b3 = (a + b)(a2 – ab + b2) a3 - b3 = (a – b)(a2 + ab + b2)**Rational expressions**• Let’s divide polynomials by other polynomials. • What are the restrictions on x? • Finish logistics…**Rational expressions**Let’s divide polynomials by other polynomials. What are the restrictions on x? Finish logistics…