Factoring Polynomials Using GCF and Grouping

Factoring Quad: Quiz #4 Review/Practice

(Focus on topics covered weeks 13 & 14, including GCF, X-Method and Grouping)

Greatest Common Factor (GCF)

The highest expression that divides into the terms.

This should always be your first step, since it will start with simplest form and can make it possible to use other methods. From there, strategize about which method will be most helpful.

Multiple Choice

Factor the common factor out of each expression.

-15m⁶ - 30m⁴ - 18m³

• -3m² (5m³ + 10m + 6)

• -3m⁴ (m³ + 5m + 6)

• -3m³ (5m⁴ + 10m + 6)

• -3m³ (5m³ +10m + 6)

Fill in the Blank

What is the GCF of the following?

$$12x^3+9yx$$  

Multiple Choice

What is the first question you ask yourself when factoring a polynomial? 

• How many terms does it have? 
• Is there a GCF? 
• What strategy should I use? 
• Why do I have to learn this?!?!?!

Multiple Choice

Factor:
2n³+16n+12

• 2n(n³+24n+6)
• 2(n³+8n+6)
• 2n(n³+8n+6)
• 3(n³+8n+6)

Multiple Choice

Factor:
56a³-8a

• 8a²(56a³-8a)
• 8a(7a²-1)
• 8a(7a³-a)
• 8a²(35a²-a)

Magic X

1st: make sure there is no GCF

2nd: multiply the a and c (ax²+bx+c)

and identify the b.

3rd: find factors of ab that you can "add" to get b.

4th: divide each of the factors by "a"

5th: remember "bottoms up" when writing your "binomial X binomial answer.

Multiple Choice

What is (a)*(c) 
in the quadratic y=4x²+9x+5

• 4*9 = 36
• 4*5 = 20
• 9*5 = 45
• 16*5 = 80

Multiple Choice

Factor
9x²-6x-8

• (3x+2)(3x-4)
• (3x+2)(3x+4)
• (3x-2)(3x-4)
• (x-1)(9x+8)

Multiple Choice

Factor
2x² - 13x - 70

• (2x-7)(x+10)
• (7x+5)(x+2)
• (2x+7)(x-10)
• 2(x+7)(x+10)

Multiple Choice

Factor
3v² - 4v - 7

• (3v-7)(v+1)
• 3(v-7)(v-1)
• (3v+1)(v-9)
• (3v+1)(v-10)

Multiple Choice

Factor:
 2m² + 3m - 9

• 2(m + 3)(m - 3)
• (2m - 3)²
• (m + 3)(2m - 3)
• (2m + 3)(m - 3)

Factor by Grouping

1st: Split up your polynomial into 2 sections.

2nd: Factor out the GCF from each group.

3rd: write your answer in (binomial)x(binomial) form.

Multiple Choice

Factor by grouping:

5n³-10n²+3n-6

• (5n²+3)(n-2)

• (5n²-3)(n-2)

• (5n³+3)(n-2)

• 10n(n²-6)

Multiple Choice

Factor Completely!!!

• A
• B
• C
• D

Multiple Choice

2x³-8x²-x+4

• (2x²-1)(x-4)
• 2(x²-1)(x+4)
• (x²-1)(2x-4)
• (2x²+1)(x-4)

Multiple Choice

Factor by grouping:

4p³+8p²+3p+6

• (2p²+3)(p+2)

• (2p²+6)(p+4)

• (4p²+3)(p+2)

• (4p²+8p)(3p+6)

Open Ended

ALMOST DONE...

What will you do to prepare for our next quiz?