Polynomial Theorem

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

• -25

• 25

• 113

• -113

If 𝒙²+𝟑𝒙+𝟕 is divided by  𝒙+𝟐, then what is the remainder?

• 0

• -3

• 9

• 5

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)

Use the remainder theorem to find the value of p(c): p(x) = 3x³ + 4x + 32, c = -2.

• p(-2) = 0 so

  3x³ + 4x + 32 =

  (x + 2)(3x² - 6x + 16)

• p(-2) = 0 so

  3x³ + 4x + 32 =

  (x - 2)(3x² - 6x + 16)

• p(-2) = 36

• p(-2) = 52

Use the remainder theorem to find the value of p(c): p(x) = 4x³ + 3x + 38, c = -2.

• p(-2) = 0 so

  4x³ + 3x + 38 =

  (x + 2)(4x³ - 8x + 19)

• p(-2) = 0 so

  4x³ + 3x + 38 =

  (x - 2)(4x³ - 8x + 19)

• p(-2) = 48

• p(-2) = 60

You are given a polynomial and one of its zeros. Factor the polynomial and find all of the real zeros. x³ - 6x² - x + 6, c = -1

• x³ - 6x² - x + 6 =

  (x + 1)² (x - 6); zeros are x = -1, 6

• x³ - 6x² - x + 6 =

  (x - 1)² (x - 6); zeros are x = 1, 6

• x³ - 6x² - x + 6 =

  (x + 1)(x - 1)(x - 6); zeros are x = -1, 1,-6

• x³ - 6x² - x + 6 =

  (x + 1)(x - 1)(x - 6); zeros are x = -1, 1, 6

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

Is (x-2) a factor of             f(x)= x³-8x²+14x-4?

• Yes, (x-2) is a factor. There is a remainder.

• No, (x-2) is  not a factor. The remainder is zero.

• Yes, (x-2) is a factor. The remainder is zero.

• No, (x-2) is  not a factor. There is a remainder. 

Which statement is true?

• (x-3) is a factor of (x³ - 3x² + 2x + 2)

• (x-3) is not a factor of (x³ - 3x² + 2x + 2)

• The remainder when (x³ - 3x² + 2x + 2) is divided by (x-3) is zero.

• The remainder when (x³ - 3x² + 2x + 2) is divided by (x-3) is not zero. The remainder is 17.