Product Sum Factoring Method

Methods of Factoring: Knowledge Check

By Mr. Ginarte

Draw

Draw something fun

​Starting with GCF....

Multiple Choice

Factor
12x + 9

• 3(4x + 3)
• x(12+9)
• 3(4x - 3)
• not factorable

Multiple Choice

Factor:
18a² - 15a

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

Multiple Choice

Factor by GCF

18x+7y

• 7(2x+y)

• 2(9x+4y)

• No Common Factor

• x(18+7y)

Multiple Choice

Factor:
10a⁴+16a+10a²

• 2a(5a³⁺8+5a)
• 2a⁴(5a+8a²+5a³)
• 2a⁴(10+16a+40a²)
• 3a³(5+8a+a²)

Difference of Two Squares

Multiple Choice

Factor:

$$x^2-144$$  

• (x-12)(x+12)

• (x-12)(x-12)

• (x+12)(x+12)

• Not Factorable

Multiple Choice

x² + 81

• Unfactorable

• ( x - 9 ) ( x + 9 )

• ( x + 9 ) ( x + 9 )

• ( x - 9 ) ( x - 9 )

Multiple Choice

x⁴ - 16

• ( 2x - 4) ( 2x + 4)

• ( x² - 4) ( x² + 4)

• ( x² - 8) ( x² + 8)

• ( x - 4) ( x + 4)

Multiple Choice

4x² - 64y²

• Unfactorable

• ( 2x - 32y) (2 x + 32y)

• ( 2x - 8y) (2 x - 8y)

• ( 2x - 8y) (2 x + 8y)

​Factoring Trinomials

​If Perfect Squares:

​a²+2ab+b² = (a+b)²

​

​

If not perfect squares:

Product x Sum Method

(What two numbers add to the middle term (b) but multiply to the last term (c)​

​

Multiple Choice

Factor 

$$k^2+7k+10$$  .

• $$(k+2)(k-5)$$  

• $$(k+2)(k+5)$$  

• $$(k+10)(k+4)$$  

• $$(k-2)(k-5)$$  

Multiple Choice

Factor:
 n² + 10n + 25

• (n + 5)(n - 5)
• (n + 25)(n + 1)
• (n - 5)²
• (n + 5)²

Multiple Choice

Factor $$k^2-2k-24$$  

• $$(k-4)(k+6)$$  

• $$(k+4)(k+6)$$  

• $$(k+6)(k-1)$$  

• $$(k+4)(k-6)$$  

Multiple Choice

Factor: x² + 24x + 144

• (x + 12)²
• (x + 9)²
• (x + 15)²
• (x + 13)²

Multiple Choice

Factor:

$$x^2+6x+8$$  

• $$(x+4)(x+3)$$  

• $$(x+2)(x+3)$$  

• $$(x+4)(x+2)$$  

• $$(x+5)(x+1)$$  

Multiple Choice

4x² - 25

• (2x + 5) (2x - 5)

• (2x - 5)²

• (2x + 5)²

• 2x + 5(2x - 5)