Factoring Special Cases

FACTORING

Multiple Choice

What is ALWAYS the first step when factoring?

• Look for the GCF

• Write a, b, and c

• Difference of squares

• Group

Multiple Choice

What is the GCF of 14 and 28?

• 2
• 7
• 14
• 8

Multiple Choice

Which expression is equivalent to 5x²+20x?

• 5

• x

• 5x

• 20x

Multiple Choice

Challenge Question:

What is the GCF of 26xy and 10x²y²?

• 2xy
• 2x²y²
• 10x²y²
• 10xy

Multiple Choice

What is the GCF of 32 and 40?

• 2
• 4
• 6
• 8

Multiple Choice

Factor the following binomial:

$$5a^2-15$$  

• $$5\left(a^2-15\right)$$  

• $$5a\left(a-15\right)$$  

• $$5\left(a^2-3\right)$$  

• $$5a\left(a-3\right)$$  

Factoring Special Cases

Objective: Factor special case quadratics​

REVIEW Square Roots

1² (means 1×1) = 1

2² (means 2×2) = 4

3² (means 3×3) = 9

4² (means 4×4) = 16

5² (means 5×5) = 25

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...

Match

Match the following binomials with their products.

• (x + 6)(x - 6)

• (x + 6)²

• (x - 6)²

• (x + 9)(x - 4)

• (x - 9)(x + 4)

x² - 36

x² + 12x + 36

x² - 12x + 36

x² + 5x - 36

x² - 5x - 36

• x² - 36

• x² + 12x + 36

• x² - 12x + 36

• x² + 5x - 36

• x² - 5x - 36

Factoring Special Cases

Objective: Factor special case quadratics​

EXAMPLES ​PERFECT SQUARES

​Factor: x² - 10x + 25

​Factor: x² + 3x + 9

Questions to Ask
1) Are the 1st and 3rd term perfect squares?
2) If YES, multiply them and double it. Is that the middle term?

Math Response

Factor: x² + 12x + 36

Type answer here

Correct Answer: \left(x+6\right)^2

Deg^°

Rad

EXAMPLES ​PERFECT SQUARES

​Factor: 4x² + 12x + 9

​Factor: 36x² - 48x + 16

Questions to Ask
1) Are the 1st and 3rd term perfect squares?
2) If YES, multiply them and double it. Is that the middle term?

​DIFFERENCE OF SQUARES

​Factor: x² - 81

​Factor: 64x² - 49

​Factor: x² + 9

Questions to Ask
1) Are the 1st and 3rd term perfect squares?
2) If YES, is it subtraction?

Then factor

Math Response

Factor: x² - 121

Type answer here

Correct Answer: \left(x-11\right)\left(x+11\right)

Deg^°

Rad

Math Response

Factor: 49x² - 81

Type answer here

Correct Answer: \left(7x-9\right)\left(7x+9\right)

Deg^°

Rad

Multiple Select

Which is an example of difference of two squares?

• ( x³ - 4)

• ( x² - 3)

• ( x² + 4)

• ( x² - 4)

Multiple Choice

Factor x² – 16.

• (x + 2)(x – 8)
• (x – 4)(x – 4)
• (x + 4)(x + 4)
• (x + 4)(x – 4)

Multiple Choice

Fully Factor the Following
25x²-81

• (5x-9)²
• (5x+9)(5x-9)
• 25(x-9)²
• (9x+5)(9x-5)

LET'S PRACTICE2s²

​REMEMBER:
1. Check GCF first
2. Then, check if special case OR use box method right away

Multiple Choice

Factor completely: 18x² - 8

• 2(9x² - 4)

• 2(3x +2)(3x - 2)

• 2(3x - 2)²

• 2(3x + 2)²

Multiple Choice

Factor: 
x² - 400

• ( x - 200) ( x + 200) 
• ( x + 20) ( x + 20) 
• Prime
• ( x - 20) ( x + 20) 

Multiple Choice

Factor: 
25x² - 100y²

• ( 5x - 10y) (5xy + 10y) 
• ( 5x - 10y)²
• Prime
• ( 5x - 50y) (5x + 50y) 

Multiple Choice

Factor, if possible: 
64x²-16x+1

• Not factorable.
• (32x-1)²
• (8x+1)²
• (8x-1)²

Multiple Choice

Factor

x² + 18x + 81

• (x + 9)(x – 9)

• (x + 18)²

• (x + 9)²

• (x + 6)²

Multiple Choice

Factor completely: $$8x^2-50$$  

• $$2\left(4x^2-25\right)$$  

• $$2\left(2x-5\right)^2$$  

• $$2\left(4x-5\right)\left(4x+5\right)$$  

• $$2\left(2x-5\right)\left(2x+5\right)$$  

Multiple Choice

Factor completely: $$49x^2-126x+81$$  

• $$\left(7x+9\right)^2$$  

• $$\left(7x-9\right)^2$$  

• $$\left(7x+9\right)\left(7x-9\right)$$  

• $$\left(9x-7\right)^2$$  

Multiple Choice

 Factor completely:  $$4x^2+16x+16$$  

• $$2\left(2x^2+8x+8\right)$$  

• $$4\left(x^2+4x+4\right)$$  

• $$\left(2x+4\right)^2$$  

• $$4\left(x+2\right)^2$$  

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 Choice

Factor:
3x² - 75

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