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Math Help - Need help with Factoring and Solving Equations #3.

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    Post Need help with Factoring and Solving Equations #3.

    Hi! Ive been trying to do these problems for a while and Im stumped. I finished 13 problems and fully understand them , but I don't know how to do these problems. It would be nice if you could write each step out or the answer at the very least. Or hints or tips, like which theorem or something to use. Shortcuts.

    6. Find all the roots for
    2x^4 + 11x^3 + 17x^2 - 5x - 25 = 0
    For this, how do you start it. Like what is the most efficient way. Also is there any shortcuts?

    7. f(x) = 2x + x^2 - x + 3k
    f(x) / x+2k has a remainder of -5, find k
    Last edited by mr fantastic; January 11th 2011 at 10:25 AM. Reason: dispersing questions from original thread into separate ones
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    Then for number 7.
    7. f(x) = 2x + x^2 - x + 3k
    f(x) / x+2k has a remainder of -5, find k
    What do i plug in? because it has k in the x+2k.
    i plug in x-2k? and then set it equal to -5?
    Last edited by donaldmax; January 10th 2011 at 09:57 PM. Reason: wrong number inputted
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    By the remainder theorem, the remainder of \displaystyle \frac{f(x)}{x - a} is \displaystyle f(a).

    So if you're dividing by \displaystyle x - 2k, the remainder is \displaystyle f(2k).


    So you are going to solve for \displaystyle k with \displaystyle f(2k) = -5.
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    Quote Originally Posted by donaldmax View Post
    6. Find all the roots for
    2x^4 + 11x^3 + 17x^2 - 5x - 25 = 0
    For this, how do you start it. Like what is the most efficient way. Also is there any shortcuts?
    no "shortcuts" for this one ... use the rational root theorem for possible rational roots.
    Use of the theorem let me find that x = 1 is a root.
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    Quote Originally Posted by skeeter View Post
    no "shortcuts" for this one ... use the rational root theorem for possible rational roots.
    Use of the theorem let me find that x = 1 is a root.
    Actually there's one "almost" shortcut. Substituting a 1 for x is the same as adding all the coefficients. So if all the coefficients add to 0, then x=1 is a root.
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