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Simple factoring

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Transcript

  • 1. Simple Factoring Objective: Find the greatest common factor in and factor polynomials.
  • 2. Greatest common factor (GCF)
    • The largest of the common factors of two or more numbers.
  • 3. Polynomial
    • Many terms containing a combination of variables, constants, and positive exponents that are added.
  • 4. Distributive property
    • Multiplying a single term and a polynomial.
  • 5. Distributive Property Examples and Practice To multiply common bases with exponents: Keep the base and add the exponents. x 2 (x 3 ) = x 5 y 4 (y 7 ) = y 11 z 23 (z 3 ) = z 26 Examples:   2(50 + 3) = 100 + 6 = 106   2(x + 3) = 2x + 6   y(x + 1) = yx + y   y(x + y 2 ) = yx + y 3   Practice:   3(10 + 6)     3(x + 6)   y(x + 6)   y(x + y 4 )
  • 6. Find the Greatest Common Factor Find the greatest common factor: 10 + 5 2x – 4x 3y +6y 2 8d 3 + 4d 2 + 12d
  • 7. Factoring: The distributive property in reverse:
    • Identify the GCF
    • Divide each term by the GCF
    • Place the GCF in front of parentheses
    • Place the remainder in the parentheses
    • Check: Does using the distributive property result in the original expression?
    • 3x + bx
    • GCF = x
    • 3x/x = 3
    • bx/x = b
    • 3-4) x ( 3 + b )
    • 5) 3x + bx
  • 8. Factoring Practice
    • ax – cx
    • 9x – 3y
    • ax – bx
    • 4x – 12y
    • 25y – 35y 2
    • 12y 2 – 36y 3 + 24y 4