Factor the polynomial: 64x^3 + 343

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- Jan 6th 2009, 09:15 PMmagentaritaFactor the Polynomial
Factor the polynomial: 64x^3 + 343

- Jan 6th 2009, 09:19 PMMush
Set it equal to zero and find the roots, that will give you a factor!

$\displaystyle 64x^3+343 = 0 $

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

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

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

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

The quadratic in this equation is irreducible. - Jan 6th 2009, 11:25 PMmr fantastic
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. - Jan 7th 2009, 06:42 PMmagentaritaok...