Greatest Common Factor Algebra

Section 3.11 - A common goal: Greatest Common Factor

Work through the following slides working with GCF's.

Multiple Choice

List all the factors of 12

• 1, 2, 3, 4, 6, 12
• 1, 2, 4, 12
• 1, 12
• 1, 2, 3, 4, 5, 6, 12

Multiple Choice

What is the GCF of 8 and 24?

• 1

• 24

• 8

• 4

Multiple Choice

What is the Greatest Common Factor of 12 and 48?

• 6

• 12

• 4

• 16

Multiple Choice

What is the GCF of;

2n²-8n³

• 2n

• 2n²

• n²

• 2n-4

Self - Analysis

If you got 3 or more incorrect answers, pause here and get Mrs. Gutzmer's attention. Let's figure our the disconnect. If you are good to go, please continue.

Multiple Choice

Factor:First think about the common factor between 56 and 8 AND the greatest common factor between a³ and a.

56a³-8a

• 8a²(56a³-8a)

• 8a(7a²-1)

• 8a(7a³-a)

• 8a²(35a²-a)

Multiple Choice

3x³ + 9x² - 15x 

• x(3x² + 9x - 15) 
• 3x(x² + 3x - 5)
• 3x(x² - 9x + 15) 
• x(3x² -9x + 15) 

Multiple Choice

Factor by using GCF:
8n³ + 2n²

• 2n²(4n-1)
• 2n²(4n + 1)
• n²(8n+2)
• 3n(4n+1)

Multiple Choice

Factor:
16x² + 18x + 12

• 4(4x² + 6x + 3)
• 2(8x² + 9x + 6)
• 2x(8x + 9 + 3)
• x(16x + 18 + 12)

Multiple Choice

What is the greatest common factor of the three terms in the expression?
24m³n⁵p + 6mn⁴p² + 4mn⁵

• 2mn
• 24mn⁴
• 2mn⁴
• 2mn⁴p

Factor By Grouping

• Another method of factoring that is used with an even number of terms when there is not a common factor between them all but only some.

• Example: x² + 5x + 9x + 45

Multiple Choice

Factor by grouping:

30x³+15x²-18x-9

• (5x²-3)(6x+1)

• (5x²-3)(6x+3)

• 3(5x²+3)(2x-1)

• 3(5x²-3)(2x+1)

Multiple Choice

Factor by grouping:

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:

7r³-8r²+42r-48

• (r²+6)(7r+8)

• (r²+6)(7r-8)

• (r²+6)(r²+8)

• (r²+6)(7r+6)