Factoring Completely

Factoring Completely

Steps for factoring completely

• Always look for a GCF first!!

• If 4 terms, factor by grouping

• If 3 terms, use Master Product or perfect square trinomial

• If 2 terms, look for difference of 2 squares

Factor completely: 5x² - 20

• Is there a GCF?

• Yes, 5. 5(x² - 4)

• There are 2 terms so look for difference of 2 squares.

• x² and 4 are both perfect squares and are subtracted.

• (x - 2)(x + 2)

• Don't forget the 5. 5(x + 2)(x - 2)

Multiple Choice

You try: 3x² - 27

• 3(x² - 9)

• 3(x + 3)²

• 3(x - 3)²

• 3(x + 3)(x - 3)

Multiple Choice

Try another one: 7x² + 7

• 7(x² + 1)

• 7(x + 1)²

• 7(x - 1)²

• 7(x - 1)(x + 1)

Multiple Choice

Factor completely: 18x² - 8

• 2(9x² - 4)

• 2(3x +2)(3x - 2)

• 2(3x - 2)²

• 2(3x + 2)²

Factor completely: 6x² - 10x - 24

• GCF: 2(3x² - 5x - 12)

• 3 terms so use master product.

• Factors of 36: 1 and 36, 2 and 18, 3 and 12, 4 and 9.

• Which ones subtract to give you 5? 9 and 4

• Group: (3x² - 9x)(+4x - 12)

• 3x(x - 3)+4(x - 3)

• 2(x - 3)(3x + 4)

Multiple Choice

You try: 6x² - 2x - 20

• 2(3x² - x - 10)

• 2(x + 2)(3x - 5)

• 2(x - 2)(3x - 5)

• 2(x - 2)(3x + 5)

Multiple Choice

How about this one: 6x² + 21x + 15

• 3(2x² +7x + 5)

• 3(x + 1)(2x + 5)

• (3x + 3)(2x + 5)

• (x - 1)(6x + 15)

Factor: 32x³ + 8x² + 48x + 12

• GCF: 4(8x³ + 2x² + 12x + 3)

• 4 terms, Grouping: (8x³ + 2x²)(+12x + 3)

• 2x²(4x + 1)+3(4x + 1)

• (4x + 1)(2x² + 3)

• Don't forget about your GCF

• 4(4x + 1)(2x³ + 3)

Multiple Choice

You try: 12x³ - 8x² + 30x - 20

• (3x - 2)(4x²+10)

• 2(3x - 2)(2x² + 5)

• 2(3x - 2)(2x + 5)

• (6x - 4)(2x² + 5)

Poll

How do you feel about factoring?

• I have no idea what I am doing.

• I'm confused but starting to understand.

• I am somewhat confident in what we are doing.

• I could teach this!