Polynomial Division & Remainder Theorem

• 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)

• 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) = 2x² - 3x + 1, c = 4.

• p(4) = 45

• p(4) = -43

• p(4) = 21

• p(4) = -19

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

You are given a polynomial and one of its zeros.

Factor the polynomial and find all of the real zeros.

x³ - 6x² + 11x - 6, c = 1

• x³ - 6x² + 11x - 6 =

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

• x³ - 6x² + 11x - 6 =

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

• x³ - 6x² + 11x - 6 =

  (x - 1)(x - 2)(x - 3); zeros are x = 1, 2,3

• x³ - 6x² + 11x - 6 =

  (x + 1)(x - 2)(x - 3); zeros are x = -1, 2, 3

What could be the equation for this polynomial?

• (x - 1) (x + 1)²

• (x + 1) (x - 1)²

• (x - 1)(x + 1)

• x² - 1