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Math Help - Factor the Polynomial

  1. #1
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    Factor the Polynomial

    Factor the polynomial: 64x^3 + 343
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  2. #2
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    Quote Originally Posted by magentarita View Post
    Factor the polynomial: 64x^3 + 343
    Set it equal to zero and find the roots, that will give you a factor!

     64x^3+343 = 0
    x = (\frac{-343}{64})^{\frac{1}{3}} = -\frac{7}{4}

    Hence x +\frac{7}{4} is a factor.

    Use long division to find f(x) such that (x+\frac{7}{4})f(x) = 64x^3+343

    You should get (x+\frac{7}{4})(64x^2+112x+196) = 64x^3+343

    The quadratic in this equation is irreducible.
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  3. #3
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    Quote Originally Posted by magentarita View Post
    Factor the polynomial: 64x^3 + 343
    You have (4x)^3 + 7^3. Now use the sum of cubes formula for factorising: Sum of Cubes

    Note that the quadratic factor in this formula cannot be further factorised.
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  4. #4
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    ok...

    Quote Originally Posted by mr fantastic View Post
    You have (4x)^3 + 7^3. Now use the sum of cubes formula for factorising: Sum of Cubes

    Note that the quadratic factor in this formula cannot be further factorised.
    I can take it from here.
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