Solve 7k^3+56

$$7 k ^ { 3 } + 56$$

Factor

$$7\left(k+2\right)\left(k^{2}-2k+4\right)$$

Solution Steps

Factor out 7.

$$7\left(k^{3}+8\right)$$

Consider k^{3}+8. Rewrite k^{3}+8 as k^{3}+2^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

$$\left(k+2\right)\left(k^{2}-2k+4\right)$$

Rewrite the complete factored expression. Polynomial k^{2}-2k+4 is not factored since it does not have any rational roots.

$$7\left(k+2\right)\left(k^{2}-2k+4\right)$$

Evaluate

$$7\left(k^{3}+8\right)$$