Unit 2 - Algebra & Factoring

Cohort A Unit Test Brainstorming...

Q. Why do we test you?

  • To check for understanding

    • Teacher (a little - so I can help you)

    • Students (feedback)

    • Parents (feedback)

  • To help prepare for the exam... college, university... life?

  • Pinpoint errors in my teaching or your learning - so we can improve

Q. What would we assess on the Unit 2 test?

  • 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)