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Math Help - Questions Involving Dividing Polynomials

  1. #1
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    Questions Involving Dividing Polynomials

    1) 8x^3 + 10x^2 - px - 5 is divisible by 2x+1. There is no remainder. Find the value of p.

    2) When x^6 + x^4 - 2x^2 + k is divided by 1 + x^2, the remainder is 5. Find the value of k.

    3) The volume of a cylindrical can is (4πx^3 + 28πx^2 + 65πx + 50π) cm^3. The can is (x +2) cm high. What is the radius?

    If anyone can help me out with any of these questions I would really appreciate it! Thanks in advance! Just to clarify, "π" is pi.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Questions Involving Dividing Polynomials

    1.) Let f(x)=8x^3+10x^2-px-5

    From the given information, we know from the remainder theorem we must have:

    f\left(-\frac{1}{2} \right)=0

    From this you can find p.

    2.) Let u=x^2 and f(u)=u^3 + u^2 - 2u + k

    By the remainder theorem and the given information, we know:

    f(-1)=5

    From this you can find k.

    3.) The volume of the can is:

    V=\pi r^2h=\pi r^2(x+2)=\pi(4x^3 + 28x^2 + 65x + 50)

    From this you may determine r(x). Check to see if the cubic has -2 as a root.
    Thanks from misiaizeska
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  3. #3
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    Re: Questions Involving Dividing Polynomials

    Thank you so much!
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