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Math Help - How do you factor x^3+7x^2+8x-16?

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    How do you factor x^3+7x^2+8x-16?

    How do you factor x^3+7x^2+8x-16?

    Thanks.
    Last edited by mr fantastic; September 27th 2011 at 03:09 AM. Reason: Copied title into main body of post.
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    Re: How do you factor x^3+7x^2+8x-16?

    First thing to do is find factors of -16. Can you list them?
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    Re: How do you factor x^3+7x^2+8x-16?

    Quote Originally Posted by pickslides View Post
    First thing to do is find factors of -16. Can you list them?
    -16 has the factors of the following: 2, 4, 8, 16.
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    Re: How do you factor x^3+7x^2+8x-16?

    Quote Originally Posted by david213 View Post
    -16 has the factors of the following: 2, 4, 8, 16.
    Also, -1,1,-2,-4,-8 and -16.

    Now substitute these values into the equation like this

    x=2: 2^3+7(2)^2+8(2)-16 = 36

    what are the other results?
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    Re: How do you factor x^3+7x^2+8x-16?

    I kinda have a clue right now. So you are trying to get the number that will make the equation equals to zero? I plugged all these numbers into my calculator, and it turns out that 1 will make the equation equals to zero.
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    Re: How do you factor x^3+7x^2+8x-16?

    Quote Originally Posted by david213 View Post
    I kinda have a clue right now. So you are trying to get the number that will make the equation equals to zero? I plugged all these numbers into my calculator, and it turns out that 1 will make the equation equals to zero.
    Yes, so since f(1) = 0, that means (x - 1) is a factor. So now long divide...
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    Re: How do you factor x^3+7x^2+8x-16?

    Quote Originally Posted by david213 View Post
    I kinda have a clue right now. So you are trying to get the number that will make the equation equals to zero?
    Yep!

    The factor theorem says: For f(x), if f(a)=0 then x-a is a factor.


    Quote Originally Posted by david213 View Post
    I plugged all these numbers into my calculator, and it turns out that 1 will make the equation equals to zero.
    Great, so therefore (x-1) is a factor.

    Now find \displaystyle \frac{x^3+7x^2+8x-16}{x-1}= \dots and you are done!
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    Re: How do you factor x^3+7x^2+8x-16?

    Quote Originally Posted by pickslides View Post
    Yep!

    The factor theorem says: For f(x), if f(a)=0 then x-a is a factor.




    Great, so therefore (x-1) is a factor.

    Now find \displaystyle \frac{x^3+7x^2+8x-16}{x-1}= \dots and you are done!
    ALMOST done, you probably still have to factorise the resulting quadratic factor...
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    Re: How do you factor x^3+7x^2+8x-16?

    Okay, so, after I did the long division, I got x^2+8x+16. Thus, the the factored form of x^3+7x^2+8x-16 is (x-1)(x+4)^2?
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    Re: How do you factor x^3+7x^2+8x-16?

    Well done, you can expand it back out to check.
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    Re: How do you factor x^3+7x^2+8x-16?

    Quote Originally Posted by pickslides View Post
    First thing to do is find factors of -16. Can you list them?
    Youn should provide the reason for this, though perhaps asking the OP to tell us what they have tried should also be considered?

    - "The rational root theorem tells you that if this has any "nice" roots/factor that the roots are factors of -16"

    CB
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