# Factor the Polynomial

• Jan 6th 2009, 09:15 PM
magentarita
Factor the Polynomial
Factor the polynomial: 64x^3 + 343
• Jan 6th 2009, 09:19 PM
Mush
Quote:

Originally Posted by magentarita
Factor the polynomial: 64x^3 + 343

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 PM
mr fantastic
Quote:

Originally Posted by magentarita
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.
• Jan 7th 2009, 06:42 PM
magentarita
ok...
Quote:

Originally Posted by mr 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.

I can take it from here.