Warm-Up Which of the following does not belong?

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Presentation transcript:

Warm-Up Which of the following does not belong? 2 17 5 23 10 59 37 3 Primes 2 17 5 23 10 59 37 3

Factoring! Objectives: To factor “special pattern” binomials

Factoring: Polynomials When factoring a polynomial, you have to write it as the product of prime polynomials. Prime factors

Flowchart A flowchart is a type of diagram that helps steer you through a complex process.

Flowchart The factoring flowchart is a simple device that will guide us through the complex process of factoring a polynomial. According to the chart, what is the first step in factoring a polynomial?

Greatest Common Factor The fist step in factoring a polynomial is to use the distributive property backwards to take out the greatest common factor. Quotient GCF Taking out the GCF first will make factoring the rest of the polynomial much easier.

Factoring: Polynomials If your polynomial has no GCF or you’ve already factored it out, what is the next step in factoring your polynomial?

Factoring: Polynomials The next step depends on how many terms your polynomial has: 2, 3, or 4 or more.

Factoring: Binomials The binomial case is easy; it’s based on patterns. The first is the difference of two squares: So going backwards… Square root of 2nd term Difference of 2 Squares Square root of 1st term

Difference of Two Squares

Sum of Two Squares A sum of two squares is prime! No work! Ex) Factor Prime!

Examples: Factor. 16x2 – 1 16x4 – 1 −9x2 + 4y2

Examples

Sneedlegrit: Factor. 9x2 – 4

Factoring: Polynomials If your binomial is not the difference of two squares, maybe it is the sum or difference of two cubes.

Sum or Difference of Two Cubes Sum of Two Cubes Difference of Two Cubes

Examples: Factor. x3 – 27 6x3 + 6y3

Examples Factor. 3. x3 + 1000 4. 8x3 – 27y3 5. x6 – y6

Sneedlegrit: Factor. 2. x3 – 8

HW: pg.38 (19 – 28, 39 – 46) All