Remainder / Factor Theorem

What is the proper way to write the answer for the following problem? 

• 2x³-x²-25x-12
• 2x⁴-x³-25x²-12x+0

Which term is missing in this problem?
(2x³ + 5x² + 9) ÷
(x + 3)

• x⁴
• x³
• x²
• x

What should you add to this problem?

(2x³ + 5x² + 9) ÷ (x + 3)

• 0x⁴

• 0x³

• 0x²

• 0x

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³ - 5x² + 2x - 10

• 0
• 2x-10
• -2x-10
• 2x+10

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

• -2
• -6
• -12
• 0

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

If P( -4) = 0, which of the following statements is true about P(x)?

• x+4 is a factor of P(x)

• P(x) = 0, has four negative roots

• 4 is a root of P(x) = 0

• P(0) = - 4

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

• YES
• NO

Find all the zeros, given that f(-3) = 0
f(x) = 2x³+5x²-6x-9

• -1,-3,-3
• -1,-3,3/2
• 3,3,3
• -3,2/3,-1