Rational Roots, Remainder Theorem, and Factoring Completely

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

• x + 1
• x + 2
• x + 5
• x + 10

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

• -2
• -6
• -12
• 0

Which binomial is a factor of 
f(x)= x³ + x² -24x +36?

• x + 2
• x + 3
• x + 6
• x + 9

Which binomial is a factor of 
f(x)= 6x³ -35x² +34x +40?

• 2x - 3
• 2x - 5
• 3x - 2
• 5x - 2

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25
• 25
• 113
• -113

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)

For division, what # is in the left
box?

• 0
• 1
• 2
• 3

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

• 0
• 10
• 15
• -7

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)