Polynomial Division and Remainder Theorem

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

• 4

• -4

• 8

(3x³ + 5x - 1) ÷ (x + 1)

• 3x³ - 3x² + 8x - 9

• 3x² - 3x + 8 - 9/x+1

• 3x² + 3x + 8 + 7/x+1

• 3x³ + 3x² + 8x + 7

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

• 3x³ - 5x² - 2x + 8

• 3x² + x - 6

• 3x² - 5x - 2 + 8/x+1

• 3x³ + x² - 6x

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

• 3   0   -4   6   1

• 6   -4   3   1   0

• 6   -4   0   3   1

• -6   4   0   -3   -1

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

• 0

• 2

• 4

• 6

For synthetic division, what would be the number in the left hand box?

• 0

• 1

• 2

• 3

x - 7 x² - 7 x + 7 x² + 3x - 54

• x - 7

• x² - 7

• x + 7

• x² + 3x - 54

• x + 5 + (2/2x - 4)
• x - 8
• x - 5 + (3/2x - 4)
• x + 5

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

2x³ - 5x - 7 ÷
x - 2

• 2x³ - 4x² + 3x - 13

• 2x³ + 4x² +3x - 1

• 2x² - 4x + 3 - 13/x-2

• 2x² + 4x + 3 - 1/x-2