Factoring Difference of Squares & GCF

What is the GCF? 

 $5x^2+20x$  

• 5

• x

• 5x

• 20x

What is the GCF? 

 $3x^2-2x$  

• 3

• 3x

• x

• 2

Factor by using GCF:

 $8n^3+2n^2$  

• 2n²(4n-1)

• 2n²(4n + 1)

• n²(8n+2)

• 3n(4n+1)

Factor using GCF:  

 $3x^3+9x^2-15x$  

• x(3x² + 9x - 15) 

• 3x(x² + 3x - 5)

• 3x(x² - 9x + 15) 

• x(3x² -9x + 15) 

Ms. Lee is trying to factor this polynomial.

 $18x^2y\ +\ 36x^6y^3$ 

She wrote on the board that the GCF is:  $9x^2y^3$  
Is she correct?

• Yes, because 9 is the GCF of 18 and 36, and there is a  $x^2$  and $y^3$  in the polynomial.

• Yes, because the teacher is always right!

• No. The smallest exponent for  $y$  is  $y^1$  and so the GCF is actually  $9x^2y$ 

• No, because 9 doesn't divide into 18 and 36. There are too many variables.

What is ALWAYS the first step when factoring?

• Look for the GCF

• Write a, b, and c

• Difference of squares

• Use the X-Puzzle

Factor x²-25

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• Prime

32n² - 50
(Check for a GCF)

• (16n - 25)(16n + 25)
• 2(8n - 25)(8n + 25)
• 2(4n + 5)(4n - 5)
• Not Factorable

36m² - 9
(Check for a GCF)

• (6m + 3)(6m - 3)
• 9(4m² - 1)
• 9(2m - 1)(2m + 1)
• Not Factorable

Factor

x² - 25

• ( x + 5 ) ( x - 5 )

• ( x - 5 ) ( x - 5 )

• ( x + 5 ) ( x + 5 )

• Does not factor (prime)