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Math Help - A Worksheet of Epic Proportions

  1. #1
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    Joined
    Dec 2007
    Posts
    5

    A Worksheet of Epic Proportions

    Ok not really but I do need help. There's actually three problems, after reading the rules it states one problem per thread, so if you feel like not answering the second and third one I'll just make two other threads if you wish. Thanks for your help you guys this worksheet has been impossible for me!

    Here's how the worksheet is setup:

    Before you do all the work involved in solving a multiple-choice problem, you
    usually can eliminate some answer choices.This can save you time in arriving at the
    answer to the problem, or in making an “educated” guess if you do not actually
    know how to find the answer.

    EXAMPLE 1
    One factor of x3 + x2 + x - 3 is x - 1.What is the other factor?
    A. x2 + 2x - 3 B. x2 + 2x + 3 C. x3 + 2x + 3 D. x2 - 2x + 3
    Look at the degrees of the polynomials. The original polynomial has degree 3 and
    the given factor has degree 1.The answer must have degree 3 - 1 = 2. Since
    answer choice C has degree 3, you can eliminate choice C.
    Look at the constant terms of the polynomials. The constant term of the original
    polynomial is -3. Since the constant term of the factor is -1, the other constant
    term must be 3 for the product of the two factors to be -3.The constant term of
    answer choice A is -3, so you can eliminate choice A.
    The correct answer is either B or D.

    EXAMPLE 2
    (3x + 5)(x - 2) = j
    A. 3x2 - 2x - 10 B. 3x2 - 5x - 2 C. 3x2 + 2x - 10 D. 3x2 - x - 10
    Substitute a number. The original polynomial has x - 2 as a factor. If you let x
    equal 2, then the polynomial will equal 0.The correct answer will have to equal 0
    when x is 2.
    Choice A: 3(2)2 - 2(2) - 10 = 3(4) - 4 - 10 = 12 - 4 - 10 = -2. You can eliminate A.
    Choice B: 3(2)2 - 5(2) - 2 = 3(4) - 10 - 2 = 12 - 10 - 2 = 0. B is a possible answer.
    Choice C: 3(2)2 + 2(2) - 10 = 3(4) + 4 - 10 = 12 + 4 - 10 = 6. You can eliminate C.
    Choice D: 3(2)2 - 2 - 10 = 3(4) - 2 - 10 = 12 - 2 - 10 = 0. D is a possible answer.
    The correct answer is either B or D.

    EXERCISES
    1. Multiply x - 1 by choices B and D in Example 1 to find the correct answer.

    2. Look at the constant terms in choices B and D in Example 2, and explain why
    you can eliminate choice B.

    3. Consider the following multiple-choice problem.
    One factor of 3x3 + 2x2 + x - 6 is x - 1.What is the other factor?
    F. 3x2 - 5x - 6 G. 3x2 + 5x + 6 H. 3x3 + x2 - 3 I. 3x2 - 5x + 6
    a. Explain why you can eliminate answer choices F and H.
    b. What is the correct answer to the problem?

    Once again guys thanks a million for this.
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  2. #2
    Senior Member
    Joined
    Feb 2008
    From
    Berkeley, Illinois
    Posts
    364
    For this problem, (3x + 5)(x - 2) = j, the answer is D. Go here:

    Multiplying 2 Binomials

    It will show you the answer and the homework. Let me know if you have questions.
    Last edited by mathceleb; April 22nd 2009 at 05:40 AM.
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