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4 ESO Academics - Unit 03 - Exercises 4.3.3 - Division of Polynomials. Ruffini´s Rule.

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4 ESO Academics - Unit 03 - Exercises 4.3.3 - Division of Polynomials. Ruffini´s Rule.

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UNIT 03 December 1. Solve these divisions and write the remainder and the quotient. Check the result. a) (𝟓𝟓𝒙𝒙𝟐𝟐 + 𝟕𝟕𝟕𝟕 − 𝟑𝟑) ÷ (𝒙𝒙 + 𝟑𝟑) b) (𝒙𝒙𝟑𝟑 − 𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐 − 𝟏𝟏) ÷ (𝒙𝒙 − 𝟏𝟏) c) (𝟐𝟐𝒙𝒙𝟒𝟒 − 𝟑𝟑𝒙𝒙𝟑𝟑 + 𝟓𝟓𝟓𝟓 + 𝟒𝟒) ÷ (𝒙𝒙𝟐𝟐 + 𝟐𝟐) d) (−𝟑𝟑𝒙𝒙𝟒𝟒 + 𝟐𝟐𝒙𝒙𝟑𝟑 + 𝟓𝟓𝟓𝟓 + 𝟒𝟒) ÷ (𝒙𝒙𝟐𝟐 − 𝟑𝟑) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.1
UNIT 03 December 2. Calculate m knowing that the remainder of the division is 5. (𝟑𝟑𝒙𝒙𝟒𝟒 − 𝒎𝒎) ÷ (𝒙𝒙𝟐𝟐 + 𝟏𝟏) 3. Apply Ruffini´s rule to solve these divisions: a) (𝟐𝟐𝒙𝒙𝟑𝟑 − 𝟒𝟒𝒙𝒙𝟐𝟐 − 𝟔𝟔𝟔𝟔 + 𝟖𝟖) ÷ (𝒙𝒙 + 𝟏𝟏) b) (−𝟓𝟓𝒙𝒙𝟑𝟑 + 𝟐𝟐𝒙𝒙𝟐𝟐 − 𝒙𝒙 + 𝟑𝟑) ÷ (𝒙𝒙 − 𝟐𝟐) c) (𝒙𝒙𝟒𝟒 + 𝟑𝟑𝒙𝒙𝟑𝟑 − 𝟓𝟓𝒙𝒙𝟐𝟐 + 𝒙𝒙 − 𝟕𝟕) ÷ (𝒙𝒙 + 𝟑𝟑) d) (𝟐𝟐𝒙𝒙𝟒𝟒 − 𝒙𝒙𝟑𝟑 + 𝟔𝟔𝒙𝒙𝟐𝟐 − 𝟑𝟑𝟑𝟑 + 𝟏𝟏) ÷ (𝒙𝒙 + 𝟐𝟐) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.2
UNIT 03 December e) (𝒙𝒙𝟒𝟒 − 𝒙𝒙𝟑𝟑 + 𝒙𝒙𝟐𝟐 − 𝒙𝒙 + 𝟏𝟏) ÷ (𝒙𝒙 − 𝟏𝟏) f) �−𝒙𝒙𝟓𝟓 + 𝟐𝟐𝒙𝒙𝟒𝟒 − 𝒙𝒙𝟑𝟑 + 𝟐𝟐𝒙𝒙𝟐𝟐 − 𝒙𝒙 − 𝟏𝟏� ÷ (𝒙𝒙 − 𝟑𝟑) 4. Indicate the quotient and the remainder of these divisions: a) (𝟓𝟓𝒙𝒙𝟒𝟒 + 𝟑𝟑𝟑𝟑 − 𝟓𝟓) ÷ (𝒙𝒙 + 𝟏𝟏) b) (𝟐𝟐𝒙𝒙𝟐𝟐 + 𝒙𝒙 + 𝟒𝟒 − 𝟑𝟑𝒙𝒙𝟑𝟑) ÷ (𝒙𝒙 − 𝟓𝟓) c) �−𝒙𝒙𝟑𝟑 + 𝟐𝟐𝒙𝒙𝟓𝟓 + 𝟏𝟏� ÷ (𝒙𝒙 − 𝟏𝟏) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.3
UNIT 03 December d) (𝟓𝟓𝟓𝟓 − 𝟑𝟑𝒙𝒙𝟐𝟐 + 𝟐𝟐𝒙𝒙𝟑𝟑) ÷ (𝒙𝒙 + 𝟐𝟐) 5. Using Ruffini´s rule, find m to have −𝟒𝟒 as remainder of the division: (𝟕𝟕𝒙𝒙𝟑𝟑 − 𝟓𝟓𝟓𝟓𝟓𝟓 − 𝟐𝟐) ÷ (𝒙𝒙 + 𝟏𝟏) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.4

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4 ESO Academics - Unit 03 - Exercises 4.3.3 - Division of Polynomials. Ruffini´s Rule.

  • 1. UNIT 03 December 1. Solve these divisions and write the remainder and the quotient. Check the result. a) (𝟓𝟓𝒙𝒙𝟐𝟐 + 𝟕𝟕𝟕𝟕 − 𝟑𝟑) ÷ (𝒙𝒙 + 𝟑𝟑) b) (𝒙𝒙𝟑𝟑 − 𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐 − 𝟏𝟏) ÷ (𝒙𝒙 − 𝟏𝟏) c) (𝟐𝟐𝒙𝒙𝟒𝟒 − 𝟑𝟑𝒙𝒙𝟑𝟑 + 𝟓𝟓𝟓𝟓 + 𝟒𝟒) ÷ (𝒙𝒙𝟐𝟐 + 𝟐𝟐) d) (−𝟑𝟑𝒙𝒙𝟒𝟒 + 𝟐𝟐𝒙𝒙𝟑𝟑 + 𝟓𝟓𝟓𝟓 + 𝟒𝟒) ÷ (𝒙𝒙𝟐𝟐 − 𝟑𝟑) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.1
  • 2. UNIT 03 December 2. Calculate m knowing that the remainder of the division is 5. (𝟑𝟑𝒙𝒙𝟒𝟒 − 𝒎𝒎) ÷ (𝒙𝒙𝟐𝟐 + 𝟏𝟏) 3. Apply Ruffini´s rule to solve these divisions: a) (𝟐𝟐𝒙𝒙𝟑𝟑 − 𝟒𝟒𝒙𝒙𝟐𝟐 − 𝟔𝟔𝟔𝟔 + 𝟖𝟖) ÷ (𝒙𝒙 + 𝟏𝟏) b) (−𝟓𝟓𝒙𝒙𝟑𝟑 + 𝟐𝟐𝒙𝒙𝟐𝟐 − 𝒙𝒙 + 𝟑𝟑) ÷ (𝒙𝒙 − 𝟐𝟐) c) (𝒙𝒙𝟒𝟒 + 𝟑𝟑𝒙𝒙𝟑𝟑 − 𝟓𝟓𝒙𝒙𝟐𝟐 + 𝒙𝒙 − 𝟕𝟕) ÷ (𝒙𝒙 + 𝟑𝟑) d) (𝟐𝟐𝒙𝒙𝟒𝟒 − 𝒙𝒙𝟑𝟑 + 𝟔𝟔𝒙𝒙𝟐𝟐 − 𝟑𝟑𝟑𝟑 + 𝟏𝟏) ÷ (𝒙𝒙 + 𝟐𝟐) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.2
  • 3. UNIT 03 December e) (𝒙𝒙𝟒𝟒 − 𝒙𝒙𝟑𝟑 + 𝒙𝒙𝟐𝟐 − 𝒙𝒙 + 𝟏𝟏) ÷ (𝒙𝒙 − 𝟏𝟏) f) �−𝒙𝒙𝟓𝟓 + 𝟐𝟐𝒙𝒙𝟒𝟒 − 𝒙𝒙𝟑𝟑 + 𝟐𝟐𝒙𝒙𝟐𝟐 − 𝒙𝒙 − 𝟏𝟏� ÷ (𝒙𝒙 − 𝟑𝟑) 4. Indicate the quotient and the remainder of these divisions: a) (𝟓𝟓𝒙𝒙𝟒𝟒 + 𝟑𝟑𝟑𝟑 − 𝟓𝟓) ÷ (𝒙𝒙 + 𝟏𝟏) b) (𝟐𝟐𝒙𝒙𝟐𝟐 + 𝒙𝒙 + 𝟒𝟒 − 𝟑𝟑𝒙𝒙𝟑𝟑) ÷ (𝒙𝒙 − 𝟓𝟓) c) �−𝒙𝒙𝟑𝟑 + 𝟐𝟐𝒙𝒙𝟓𝟓 + 𝟏𝟏� ÷ (𝒙𝒙 − 𝟏𝟏) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.3
  • 4. UNIT 03 December d) (𝟓𝟓𝟓𝟓 − 𝟑𝟑𝒙𝒙𝟐𝟐 + 𝟐𝟐𝒙𝒙𝟑𝟑) ÷ (𝒙𝒙 + 𝟐𝟐) 5. Using Ruffini´s rule, find m to have −𝟒𝟒 as remainder of the division: (𝟕𝟕𝒙𝒙𝟑𝟑 − 𝟓𝟓𝟓𝟓𝟓𝟓 − 𝟐𝟐) ÷ (𝒙𝒙 + 𝟏𝟏) Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.3.4