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Math Help - polynomial

  1. #1
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    polynomial

    hi, i really wanna ask a question is there any easier way to factor this polynomial 6x^4 + x^3 - 8x ^2 -x + 2 ,
    and i have one more question, when do use the integral zero theorm P (b)=0and the factor theorm P ( b/a ) = 0. i just wanna know the difference , and when to use which. thanks
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  2. #2
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    Quote Originally Posted by lickman View Post
    hi, i really wanna ask a question is there any easier way to factor this polynomial 6x^4 + x^3 - 8x ^2 -x + 2 ,
    and i have one more question, when do use the integral zero theorm P (b)=0and the factor theorm P ( b/a ) = 0. i just wanna know the difference , and when to use which. thanks
    <br />
f(x) = 6x^4+x^3-8x^2-x+2

    If you put x=1 and x=-1 in the function , it becomes 0. so the factors (x-1) and (x+1) are the factors of f(x).

    Now divide f(x) with the product =(x-1)(x+1) = x^2 - 1, we get a quadratic,

    6x^2+x-2

    Now factor the quadratic

    6x^2+x-2= (2x-1)(3x+2)

    so, factors are

    f(x) = 6x^4+x^3-8x^2-x+2=(x-1)(x+1)(2x-1)(3x+2)
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  3. #3
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    thanks alot, dividng is such a long procedure, lol. i have one more question about the P(B) = 0 and P(B/A) = 0, when do u include a and when do u only use B ? i often get confuse on trying to find the root with those
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  4. #4
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    Quote Originally Posted by lickman View Post
    thanks alot, dividng is such a long procedure, lol. i have one more question about the P(B) = 0 and P(B/A) = 0, when do u include a and when do u only use B ? i often get confuse on trying to find the root with those
    There might be times when substituting integer values into the polynomial won't give 0 as a result. If this is the case (and you can probably tell by the constant term, if it's a fraction) then you might need to substitute fractions.
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