Algebraic Expressions Factoring and Simplifying (1.3)

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Presentation transcript:

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. Ifthen P = How did you get your answer?

SAT Question #2 Send your responses via Navigator. Iffind 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. a n x n + a n-1 x n-1 + a n-2 x n-2 + a n-3 x n-3 + … a 1 x + a 0 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. x 2 + x - 6 6x 2 - 7x x x 2 y + 27xy 2 a 3 + b 3 a 3 - b 3

Factoring– the opposite of multiplying What’s the first rule in factoring? Try these. You can verify your answers with CAS. x 2 + x – 6 = (x + 3)(x – 2) 6x 2 - 7x – 3 = (2x – 3)(3x + 1) 12x x 2 y + 27xy 2 = 3x(4x 2 – 12xy + 9y 2 ) = 3x(2x – 3) 2 a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) a 3 - b 3 = (a – b)(a 2 + ab + b 2 )

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…