Dividing Polynomials by Monomials
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Questions and Answers

What does the sum of the quotients give us in polynomial division by a linear polynomial?

  • The quotient
  • The whole dividend (correct)
  • The remainder
  • The divisor

    • What does the equation $p(x) = g(x)q(x) + r(x)$ represent?

  • Division Algorithm (correct)
  • Roots of a Polynomial
  • Remainder Theorem
  • Factorization Method

    • What characterizes the remainder in polynomial division according to the text?

  • Degree less than divisor (correct)
  • Degree greater than divisor
  • Equivalent to the quotient
  • Always zero

    • In polynomial division, what does replacing $x$ by a certain value help determine?

    <p>Remainder</p> Signup and view all the answers

    What does the Remainder Theorem state?

    <p>$p(x)$ divided by $g(x)$ gives $q(x)$ as quotient and $r(x)$ as remainder</p> Signup and view all the answers

    When dividing $3x^4 - 4x^3 - 3x - 1$ by $x - 1$, what will be the remainder?

    <p>$-1$</p> Signup and view all the answers

    What is the link between the remainder in polynomial division and the value of the polynomial at a certain point?

    <p>They are equal</p> Signup and view all the answers

    What does the proof of Remainder Theorem involve according to the text?

    <p>Long division of polynomials</p> Signup and view all the answers

    $p(-1)$ for $p(x) = 3x^2 + x - 1$ gives what information about polynomial division?

    <p>$p(-1)$ equals $-1$, which is the remainder after division by $x + 1$</p> Signup and view all the answers

    What is the relationship between degree of remainder and degree of divisor in polynomial division?

    <p>The degree of remainder is less than degree of divisor.</p> Signup and view all the answers

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