# Unit 2 - Algebra & Factoring

**Cohort A Unit Test Brainstorming...**

**Cohort A Unit Test Brainstorming...**

**Q. **Why do we test you?

**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?

**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)