Polynomial Long Division and Remainder Theorem

Is (x + 2) a factor of the polynomial:

x⁴ + x³ - 2x² + 3x + 7, and what was the remainder?

• no, R=1

• yes, R=0

• no, R=29

• yes, R=5

• remainder is 8

• remainder is -2

• remainder is 0

• remainder is 6

• remainder is 0

• remainder is 2

• remainder is -28

• remainder is 24

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

• Yes

• No

• 8x² + 6x - 20 =

  (4x - 5)(2x - 1) - 16

• 8x² + 6x - 20 =

  (4x - 5)(2x + 4)

• 8x² + 6x - 20 =

  (4x - 5)(2x - 4)

• 8x² + 6x - 20 =

  (4x - 5)(2x - 4) - 40

• 3x³ + x² + 2x - 5 = (3x + 4)(x² + x + 1)

• 3x³ + x² + 2x - 5 = (3x + 4)(x² + x + 1) + 9x - 1

• 3x³ + x² + 2x - 5 = (3x - 2)(x² + x + 1)

• 3x³ + x² + 2x - 5 = (3x - 2)(x² + x + 1) + x - 3

• 2x³ - x + 1 = (2x - 2)(x² + x + 1) - x + 3

• 2x³ - x + 1 = (2x - 2)(x² + x + 1)

• 2x³ - x + 1 = (2x + 2)(x² + x + 1) - x - 1

• 2x³ - x + 1 = (2x + 2)(x² + x + 1)

Use the remainder theorem to find the value of p(c):

p(x) = 2x² - 3x + 1, c = 4.

• p(4) = 45

• p(4) = -43

• p(4) = 21

• p(4) = -19

• 3x² - 2x + 1 = (x - 1)(3x² + x + 2)

• 3x² - 2x + 1 = (x - 1)(3x + 1) + 2

• 3x² - 2x + 1 = (x - 1)(3x - 5) + 6

• 3x² - 2x + 1 = (x - 1)(3x² - 5x + 6)