Gr12 Mathematics: Ch 5.10 Factor Theorem
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Questions and Answers

What is the condition for cx - d to be a factor of p(x) according to the Factor Theorem?

  • If p(d/c) is a negative number
  • If p(d/c) is a positive number
  • If p(d/c) is a non-zero constant
  • If p(d/c) is zero (correct)
  • What can be concluded if p(d/c) = 0?

  • cx - d is a factor of p(x) (correct)
  • p(x) is a quadratic polynomial
  • p(x) is a linear polynomial
  • cx - d is not a factor of p(x)
  • What is the general form of a polynomial p(x) that has a factor cx - d?

  • p(x) = (cx - d) \* Q(x) (correct)
  • p(x) = Q(x) / (cx - d)
  • p(x) = cx - d + Q(x)
  • p(x) = cx - d / Q(x)
  • What is the relationship between the remainder and the Factor Theorem?

    <p>The remainder is zero if cx - d is a factor of p(x)</p> Signup and view all the answers

    What is a useful application of the Factor Theorem?

    <p>Factorizing cubic polynomials by finding one factor and then using polynomial division to find the remaining factors</p> Signup and view all the answers

    What can be concluded if p(x) has a root d/c?

    <p>cx - d is a factor of p(x)</p> Signup and view all the answers

    If p(x) is a polynomial and cx - d is a factor of p(x), what can be concluded about p(d/c)?

    <p>p(d/c) is equal to zero</p> Signup and view all the answers

    If p(x) is a polynomial and p(d/c) = 0, what can be concluded about cx - d?

    <p>cx - d is a factor of p(x)</p> Signup and view all the answers

    What is the polynomial Q(x) in the expression p(x) = (cx - d)Q(x)?

    <p>the quotient polynomial</p> Signup and view all the answers

    Why is the Factor Theorem particularly useful for factorizing cubic polynomials?

    <p>because it provides a method to find one factor and then use polynomial division to find the remaining factors</p> Signup and view all the answers

    What is the relationship between the roots of a polynomial p(x) and its factors?

    <p>if x = d/c is a root of p(x), then cx - d is a factor of p(x)</p> Signup and view all the answers

    What is a special case of the Remainder Theorem?

    <p>the Factor Theorem</p> Signup and view all the answers

    If $p(x) = x^3 + 2x^2 - 7x - 12$ and $p(-2) = 0$, what can be concluded about the factorization of $p(x)$?

    <p>$x - 2$ is a factor of $p(x)$</p> Signup and view all the answers

    If $p(x) = x^2 - 4x - 3$ and $cx - d$ is a factor of $p(x)$, what can be concluded about the value of $c$ and $d$?

    <p>$c = 1$ and $d = 3$</p> Signup and view all the answers

    If $p(x) = x^4 - 2x^3 - 3x^2 + 6x + 1$ and $p(1) = 0$, what can be concluded about the factorization of $p(x)$?

    <p>$x - 1$ is a factor of $p(x)$</p> Signup and view all the answers

    If $p(x) = 2x^3 + 5x^2 - 3x - 1$ and $cx - d$ is a factor of $p(x)$, what is the degree of the quotient polynomial $Q(x)$?

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

    If $p(x) = x^3 - 2x^2 - 5x + 6$ and $p(-3) = 0$, what can be concluded about the value of $p(-3/2)$?

    <p>$0$</p> Signup and view all the answers

    If $p(x) = x^4 - 4x^3 + 7x^2 - 12x + 9$ and $cx - d$ is a factor of $p(x)$, what can be concluded about the value of $c$ and $d$?

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

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