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Math Help - Finding value of "p" of a polynomail

  1. #1
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    Finding value of "p" of a polynomail

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

    What do I have to do to find p?
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  2. #2
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    Quote Originally Posted by Devi09 View Post
    8x^3 + 10x^2 - px -5 is divisible by 2x + 1 . There is no remainder. Find the value of P.

    What do I have to do to find p?
    Hi Devi09,

    There's a couple of things you can do here. Do you know synthetic division?

    You could use \frac{-1}{2} as your divisor and find P that way.

    Perhaps an easier method would be to act like 2x + 1 is a factor of f(x)=8x^3+10x^2-px-5 in which case x = -\frac{1}{2} is a root. (Factor Theorem)

    Now, set f(x)=0 and find f(-\frac{1}{2}). (Remainder Theorem.) f(x)=0 means when -\frac{1}{2} is substituted for x, the remainder is 0.

    Once you've substituted -\frac{1}{2} for x, you'll can solve for p.

    8(-\frac{1}{2})^3+10(-\frac{1}{2})^2-p(-\frac{1}{2})-5=0
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    I got another question. Lets say x^6 + x^4 - 2x^2 + k is divided by 1 + x^2 and the remainder is 5 and you need to find k

    So f(sqrt(-1))

    (sqrt-1)^6 + (sqrt-1)^4 - 2(sqrt-1)^2 + k = 5

    but -1 can't be square rooted so what would you do?
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    Quote Originally Posted by Devi09 View Post
    I got another question. Lets say x^6 + x^4 - 2x^2 + k is divided by 1 + x^2 and the remainder is 5 and you need to find k

    So f(sqrt(-1))

    (sqrt-1)^6 + (sqrt-1)^4 - 2(sqrt-1)^2 + k = 5

    but -1 can't be square rooted so what would you do?
    Sure you can. \sqrt{-1}=i

    (i)^6+(i)^4-2(i)^2+k=5
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    The answer to the question according to the answer section is 3. But how do you get that with these imaginary numbers?
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    Quote Originally Posted by masters View Post
    Sure you can. \sqrt{-1}=i

    (i)^6+(i)^4-2(i)^2+k=5
    Quote Originally Posted by Devi09 View Post
    The answer to the question according to the answer section is 3. But how do you get that with these imaginary numbers?

    i^6=-1
    i^4=+1
    i^2=-1

    -1+1-2(-1)+k=5

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