Unit 2 - Algebra & Factoring

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Knowledge of the Unit

Expanding & Simplifying Example: (x - 7)(x + 12)

Common Factors What is "common" between 18ax^2 and 6bx?

• GCF - looking for the GREATEST common factor.

• Factor 27xyz + 15x = 3x( 9yz + 5 )

What about 4x - 8y + 3x - 6y

• Grouping! Choice - what should you group by? (4x - 8y)+(3x - 6y)
  = 4(x - 2y) + 3(x - 2y)
  = (x - 2y)(4 + 3)
  = (x - 2y)(7)

Factoring "Quadratics": ax^2 + bx + c

• Also called a Trinomial

• Monic is when a = 1

• Non-Monic when a is not 1

• MONIC:

  • Is there a GCF? If yes, factor it out.

  • What two numbers multiply to 'c' and add to 'b'?

• NON-MONIC:

  • Is there a GCF? If yes, factor it out.

  • Factor by "decomposition" where we break-up the 'bx' into two pieces and then factor by grouping.

    • Multiply a(c) to get a new factor "m"

    • Check for factors of m that add to b

    • Break up b into two pieces and factor by grouping

• Difference of Squares

  • Actually decomposition when the b is zero.
    64x^2 - 81 = 64^2 + 0x - 81
    = (8x + 9)(8x - 9)

• Area of a Rectangle = (length)(width)

  • "Shaded Region" (see below)