Factorization with the Factor Theorem
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Questions and Answers

What is the correct factorization of y^2 - 5y + 6 using the Factor Theorem?

  • (y - 2)(y - 3) (correct)
  • (y + 2)(y - 3)
  • (y + 1)(y - 6)
  • (y - 1)(y - 6)

    • How did the Factor Theorem help in finding the factors of y^2 - 5y + 6?

  • By using the trial and error method to test all possible factor combinations.
  • By identifying that the constant term is the product of the roots of the polynomial. (correct)
  • By splitting the middle term of the polynomial to identify the root values.
  • By simplifying the polynomial expression to its simplest form.

    • Why is the splitting method deemed inappropriate for factorizing cubic polynomials initially?

  • Cubic polynomials have a more complex root structure that requires a different approach.
  • Factors of cubic polynomials need to be identified first to effectively use the splitting method. (correct)
  • It is based on trial and error, making it inefficient for cubic polynomials.
  • The splitting method may lead to multiple factor pairs that need to be refined further.

    • In the given expression ax2 + bx + c, which of the following statements is true?

    <p>b is the sum of two numbers ps and qr.</p> Signup and view all the answers

    For factorizing 6x2 + 17x + 5 using the splitting method, what are the correct pairs of factors for 30 that lead to p + q = 17?

    <p>2 and 15</p> Signup and view all the answers

    Using the Factor Theorem, if p(x) = 6x2 + 17x + 5, what are the correct roots (zeroes) of p(x)?

    <p>-1 and -5/6</p> Signup and view all the answers

    If x - 2 is a factor of the polynomial p(x) = x^3 + 4x^2 + 3x - 2, what is the value of p(2)?

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

    For the polynomial q(x) = 2x^3 - 5x^2 + 4x - 1, which one of the following is NOT a factor of q(x)?

    <p>(2x + 1)</p> Signup and view all the answers

    Given the polynomial r(x) = x^3 - 6x^2 + 11x - 6, what value of k would make (x - 2) a factor of r(x)?

    <p>-6</p> Signup and view all the answers

    If x + 3 is a factor of the polynomial s(x) = 3x^3 - x^2 - 10x + 6, what would be the result when s(-3) is calculated?

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

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