Factoring Review

Factoring Review

We have studied 4 types of factoring in the last 2 weeks:

1. GCF

2. Grouping

3. Trinomials (a=1)

4. Difference of Squares

Poll

How many eLearning assignments for this class have you completed

• All (3)

• Some (2)

• Only 1

• None

Multiple Choice

GCF of 24 and 56

• 2
• 4
• 6
• 8

Multiple Choice

What is the greatest common factor of 48x²and 32x³?

• 8x²
• 16x²
• 16x
• 96x³

Multiple Choice

What is the first step when factoring polynomials?

• Find the GCF

• List all the terms

• Make a triangle

• Write the answer

Multiple Choice

Factor 4b⁵+4b³+16b²

• 4b³(b⁴+b²+4b)

• 4b³(b⁴+4b+5)

• 4(b⁵+b³+4b²)

• 4b²(b³+b+4)

Multiple Choice

When a polynomial has 4 terms you can often factor by grouping.

Factor the following 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)

Prime Polynomials

If a polynomial cannot be factored at all it is called "PRIME"

Multiple Choice

What is a method of checking your work when factoring?

• Box Method

• asking the teacher every time

• hope you're correct

• division

Multiple Choice

Factor

k²+7k+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

Multiple Choice

Factor
a² - a - 12

• (a - 4)(a + 3)
• (a + 6)(a - 4)
• (a - 6)(a + 4)
• (a + 4)(a - 3)

Multiple Choice

Factor
x² + 9x - 36

• (x + 12)(x - 3)
• (x + 9)(x - 4)
• (x - 12)(x + 3)
• (x - 9)(x - 4)

Multiple Choice

Factoring reverses the process of what?

• Division
• Multiplication
• Addition
• Subtraction 

Multiple Choice

Factor
k² -2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

Multiple Choice

Factor
n² + 16n + 63

• (n-7)(n+4)
• (n+7)(n-9)
• (n-3)(n-10)
• (n+7)(n+9)

Multiple Choice

Factor
k²+7x+10

• (k+2)(k+5)
• (k-2)(k-5)
• (k+10)(k+4)
• (k+2)(k-5)

Multiple Choice

Factor completely. Use the perfect square chart to the left.

x² - 144

• ( x - 12 ) ²

• ( x - 12 ) ( x - 12 )

• ( x + 12 ) ( x + 12 )

• ( x + 12 ) ( x - 12 )

Multiple Choice

Factor using difference of squares pattern

x² - 25

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• Prime

Multiple Choice

Factor: x² - 16

• Prime

• ( x - 4) ( x + 4)

• ( x - 8) ( x + 8)

• ( x - 4) ( x - 4)

Multiple Choice

Factor completely. (Hint: Factor out GCF first.)

18x² - 50

• 2 ( 9x² - 25 )

• ( 3x + 5 ) ( 3x - 5 )

• 2 ( 3x + 5 ) ( 3x - 5 )

• 2 ( 3x - 5 ) ( 3x - 5 )

Multiple Choice

Factor Completely: x² - 25

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• Prime

The next slides are a mixed review of all types of factoring. These need to be written out clearly on your paper to submit at the end of class.

Please number each question, write the original, and show any necessary work.

Multiple Choice

Factor the following trinomial:

 $x^2-10x+24$  

•  $\left(x+6\right)\left(x-4\right)$  

•  $\left(x-6\right)\left(x+4\right)$  

•  $\left(x-6\right)\left(x-4\right)$  

•  $\left(x+6\right)\left(x+4\right)$  

Multiple Choice

Fully Factor the Following

16x²+25

• Prime

• (4x-5)(4x+5)

• (4x+5)(4x-5)

• (4x+5)²

Multiple Choice

Factor:
18a² - 15a

• 15a(3a-1)
• 3a(6a-1)
• 3(6a-5)
• 3a(6a-5)

Multiple Choice

Factor 12z² - 6z + 42 

• 6 (2z² - z + 7) 
• 6z (2z - z + 7) 

Multiple Choice

Factor:  x² + 9x + 18

• (x + 3)(x + 6)
• (x - 3)(x - 6)
• (x + 9)(x + 2)
• (x + 3)²

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 by grouping
x³ - 4x² -4x + 16

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

Multiple Choice

Factor:
9x² - 49

• (3x + 7)(3x - 7)
• (3x + 7)²
• (x - 7)²
• (x+7)(x-7)

Multiple Choice

Factor:
81m² - 1 

• not factorable
• (m-9)(m+9)
• 9m(9m-1)
• (9m-1)(9m+1)

Multiple Choice

Factor completely: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Not Factorable

Multiple Choice

30x³+15x²-18x-9

• (5x²-3)(6x+1)
• (5x²-3)(6x+3)
• 3(5x²+3)(2x-1)
• 3(5x²-3)(2x+1)