Solve x^3y^6z^9+1=

$$x ^ { 3 } y ^ { 6 } z ^ { 9 } + 1 =$$

Factor

$$\left(xy^{2}z^{3}+1\right)\left(x^{2}y^{4}z^{6}-xy^{2}z^{3}+1\right)$$

Solution Steps

Consider x^{3}y^{6}z^{9}+1 as a polynomial over variable x.

$$y^{6}z^{9}x^{3}+1$$

Find one factor of the form y^{k}z^{m}x^{n}+p, where y^{k}z^{m}x^{n} divides the monomial with the highest power y^{6}z^{9}x^{3} and p divides the constant factor 1. One such factor is xy^{2}z^{3}+1. Factor the polynomial by dividing it by this factor.

$$\left(xy^{2}z^{3}+1\right)\left(x^{2}y^{4}z^{6}-xy^{2}z^{3}+1\right)$$

Evaluate

$$x^{3}y^{6}z^{9}+1$$