Unit 2 - Algebra & Factoring

Q. Why do we test you?

• To check for understanding

• 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)