Polynomial long division

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Intros
Lessons
  1. Review: Long division with numbers
    long division with polynomials works in the same way as long division with numbers
    exercise:
    658 ÷ 20
    i) Operate long division
    ii) Identify:
    • Dividend:
    • Division:
    • Quotient:
    • Remainder:
    iii) Write the division statement in 2 ways.
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Examples
Lessons
  1. Use long division to divide polynomials
    Apply long division, and then use the result to write the division statement in 2 ways.
    1. (8x3โˆ’14x2+7xโˆ’1)รท(2xโˆ’5)\left( {8{x^3} - 14{x^2} + 7x - 1} \right) \div \left( {2x - 5} \right)
    2. (โˆ’x2+6xโˆ’2)รท(x)\left( { - {x^2} + 6x - 2} \right) \div \left( x \right)
  2. Watch out for "Missing Terms"! → Use "Placeholder"
    Operate long division.
    1. (29x3โˆ’12x4โˆ’x)รท(โˆ’3x+5)\left( {29{x^3} - 12{x^4} - x} \right) \div \left( { - 3x + 5} \right)
    2. (x3+5xโˆ’11)รท(xโˆ’2)\left( {{x^3} + 5x - 11} \right) \div \left( {x - 2} \right)
    3. (4x3+6x2โˆ’9x+5)รท(2x2โˆ’1)\left( {4{x^3} + 6{x^2} - 9x + 5} \right) \div \left( {2{x^2} - 1} \right)
  3. Application of a Division Statement
    Given the long division as shown:
    Polynomial long division
    Determine the polynomial P(x)P\left( x \right).
    1. Determine "Factors"
      (6x2+7xโˆ’5)รท(3x+5)\left( {6{x^2} + 7x - 5} \right) \div \left( {3x + 5} \right)
      1. Operate long division.
      2. Write the division statement.
      3. Is (3x+5)\left( {3x + 5} \right) a factor of (6x2+7xโˆ’5)\left( {6{x^2} + 7x - 5} \right)? Explain.