Solve a^6-7a^3+10

$$a ^ { 6 } - 7 a ^ { 3 } + 10$$

Factor

$$\left(a^{3}-5\right)\left(a^{3}-2\right)$$

Solution Steps

Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{6} and m divides the constant factor 10. One such factor is a^{3}-5. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: a^{3}-5,a^{3}-2.

$$\left(a^{3}-5\right)\left(a^{3}-2\right)$$

Evaluate

$$\left(a^{3}-5\right)\left(a^{3}-2\right)$$