Factorization

​Factorization

• Common factor

• difference of squares

• Sum or difference of cubes

• Trinomails as a product of binomials

• Grouping

Difference of squares

a² - b² = (a + b)(a - b)

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Multiple Choice

Factor:
x² - 25

• ( x + 5 ) ( x - 5 ) 
• ( x - 5 ) ( x - 5 ) 
• ( x + 5 ) ( x + 5 ) 
• Prime

Multiple Choice

x² - 9

• (x + 3) (x - 3)
• (x - 3) (x - 3)
• (x + 3) (x - 6)
• Can't factor using Diff. of Squares

Multiple Choice

What is the complete factorization of x⁴ -1

• (x² + 1)(x² - 1)

• (x + 1)² (x - 1)(x + 1)

• (x² + 1)(x + 1)

• (x² + 1)(x + 1)(x - 1)

Multiple Choice

Which of the following expressions would factor by difference of squares?

• $$4x^3-2x^2+6x-3$$  

• $$x^9-4$$  

• $$64x^4-81y^2$$  

• $$25x^2-9x$$  

Multiple Choice

4a² - 25

• (2a + 5) (2a - 5)
• (2a - 5) (2a - 5)
• (x + 5) (x - 5)
• Can't factor using Diff. of Squares

Multiple Choice

4m² + 49

• (2m + 7) (2m - 7)
• (2m - 7) (2m - 7)
• (m + 7) (m - 7)
• Can't factor using Diff. of Squares

​Sum or difference of cubes

​a³ + b³ = ( a + b )( a² ∓ ab + b² )

Multiple Choice

x³ - 27

• (x - 4)(x² + 4x + 16)
• (x + 3)(x² - 4x + 16)
• (x - 1)(x² + 1x + 1)
• (x - 3)(x² + 3x + 9)

Multiple Choice

8x³ + 27

• (3x - 2)(9x² + 6x + 4)
• (3x - 1)(9x² + 3x + 1)
• (2x + 3)(4x² - 6x + 9)
• (2x - 1)(4x² + 2x + 1)

Multiple Choice

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

• No

• Yes

• Yes, getting GCF first

• It is a sum of squares

Multiple Choice

27x³ - 1

• (3x - 1)(9x² + 3x + 1)
• (2x - 1)(4x² + 2x + 1)
• (3x - 2)(9x² + 6x + 4)
• (4x + 1)(16x² + 4x + 1)

​Trinomials as a product of binomials

Multiple Choice

What is the correct factorization of 7(x - 3) + y(3 - x)

• (7x + 21)(3y - xy)

• (7 - y)(x - 3)

• (7 + x)(x - 3)

• 7 + x

Multiple Choice

What is the correct factorization of x² + 17x + 30

• (x + 6)(x + 5)

• (x + 10)(x + 3)

• (x + 15)(x + 2)

• (x + 30)(x + 1)

Multiple Choice

$$a^2-10a+25$$  Factor:

• $$\left(a-5\right)\left(a+5\right)$$  

• $$\left(a+5\right)^2$$  

• $$\left(a-5\right)^2$$  

• $$\left(a-10\right)^2$$  

Multiple Select

Select the Perfect Square Trinomials from the list below

• x² + 10x + 25

• x² + 25x + 25

• x² +14x + 49

• 4x² + 12x + 9

Multiple Choice

Factor 2x² + 3x - 5

• (x - 5)(2x + 1)

• (x + 5)(2x - 1)

• (x + 1)(2x - 5)

• (x - 1)(2x + 5)