Factoring: Perfect Squares, Sums & Difference of Cubes

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:   x³ + 1

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

Tags

CCSS.HSA.APR.C.4

Factor:  27x³ + 8

• (3x + 2)(9x² - 6x + 4)
• (9x + 2)(3x² + 18x + 4)
• (3x²+4)(9x + 2)
• (27x + 8)(x² - 216x + 64)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Complete the formula
a³-b³=

• (a-b)(a²+ab+b²)
• (a+b)(a²-ab+b²)
• (a-b)(a²-ab+b²)
• (a+b)(a²+ab+b²)

Tags

CCSS.6.EE.A.2C

Factor
27x³-64

• (3x-4)(9x²+12x+16)
• (3x-4)(9x²-12x+16)
• (3x+4)(9x²-12x+16)
• (3x+4)(9x²+12x+16)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Factor using differencesum/ of cubes.  (use your notes!)
a³ + b³

• (a-b)(a²+ab+b²)
• (a+b)(a²-ab+b²)
• (a-b)(a²-ab+b²)
• (a+b)(a²+ab+b²)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Fully Factor the Following
216x³+125

• 6(x+5)³
• (6x+5)³
• (6x+5)(6x²-30x+25)
• (6x+5)(36x²-30x+25)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Is this a perfect square trinomial?
x² + 16x + 64

• Yes
• No

Tags

CCSS.8.EE.A.2

Is this a perfect square trinomial?
x² + 18x + 9

• Yes
• No

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Factor: x² - 30x + 225

• (x + 15)²
• (x - 15)²
• (x + 25)²
• (x - 25)²

Tags

CCSS.HSA.APR.C.4