Sum & Difference of Cubes/Remainder Theorem

Fully Factor the Following
216x³+125

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

Level 2 Question 11
64-27a³

• (4-3a)(9a²+12a+16)
• (3a-4)(3a²+12a+16)
• (4-3a)(3a²+12a+16)
• (4-3a)³

Fully Factor the Following
8x³-27

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

WHAT FACTORING TECHNIQUE YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF   27X³-343? 

• DIFFERENCE OF TWO CUBES
• DIFFERENCE OF TWO SQUARES 
• FACTORING BY GCF 

Factor this sum of cubes:
2x³ + 128

• 2(x³ + 64)
• (x + 4)(x² - 4x + 16)
• 2(x - 4)(x² + 4x + 16)
• 2(x + 4)(x² - 4x + 16)

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)

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)

WHAT FACTORING TECHNIQUE YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF   27a³-729? 

• FACTORING BY GCF 
• DIFFERENCE OF TWO SQUARES
• DIFFERENCE OF TWO CUBES 
• DIAMOND AND BOX METHOD 

The expression x³ ─ kx² +2x +5 leaves a remainder of 2 when divided by x ─ 3. Find the value of k.

• 4

• -4

• 8

What is the remainder when n³ - 7 is divided by n + 5 ?

• 118

• 132

• -132