The Remainder Theorem

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

• -2

• -6

• -12

• 0

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

• -25

• 25

• 113

• -113

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

• YES

• NO

Using the remainder theorem, find the value of k if the polynomial x^3 - 3x^2 + kx - 5 leaves a remainder of 4 when divided by (x - 1).

• 11

• -9

• 7

• 2

When a polynomial function f(x) is divided by
 (x - 8), the remainder is 12. 
What is f(8)?

• -8

• 8

• 12

• cannot be determined

What is the remainder if (x³ - 5x² + 2x - 10) is divided by (x - 5)?

• 0

• 4

• 7

• -1

What will be the remainder when the polynomial p(x) = 7x³-36x²-42x+30 is divided by x-6

• -2

• -4

• -1

• -6

You divide the polynomial g(x) by
(x - 3) and obtain a remainder of 9, what is g(3)?

• -3

• 3

• 9

• cannot be determined

If dividing polynomial g(x) by (x – 1) yields a remainder of 2, which must be true?

• g(1) = 2

• g(-1) = 2

• g(2) = 1

• g(2) = -1