Synthetic Division, Remainder Theorem and Factor Theorem

What are the three factors for
 (x³ -3x² -4x +12) ÷ (x + 2)?

• (x-2) (x+2) (x+3) 

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)

When p(x) = 9x⁴- 45x³ + 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

• p(2) = 656

• p(2) = 652

• p(2) = -64

• p(2) = -368

What are the three factors for
 (x³ +7x² +7x -15) ÷ (x -1)?

• (x-1) (x+5) (x-3) 

• (x-1) (x+5) (x + 3) 

• (x+1) (x+5) (x-3) 

• (x+1) (x-5) (x-3) 

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

• 0

• 10

• 15

• -7

Use synthetic division to determine f(-3), if
f(x)= (3x³ -5x² -4x +1).

• -25

• 25

• 113

• -113

Is (x-4) a factor of (x³ +x² -16x-16)?

• YES

• NO

Is (x-3) a factor of
(x³ - 3x² + 2x + 2)?

• Yes

• No

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

• 2x³ - x² + x + 9

• 2x² - x + 1

• 2x² - x + 1 + 9/x-2

• 2x² - 9x - 15 - 23/x-2

What is the remainder when a³ - 4 is divided by a+2? 

• -2

• -6

• -12

• 0

Find all the factors of   x³ -3x² -4x +12 given that -2 is a zero.

• (x-2) (x+2) (x+3) 

• (x-2) (x-2) (x+3)

• (x+2) (x+2) (x+3)

• (x-2) (x+2) (x-3)