Solve 21h^4+9h^2-9h-21h^3

$$21 h ^ { 4 } + 9 h ^ { 2 } - 9 h - 21 h ^ { 3 }$$

Factor

$$3h\left(h-1\right)\left(7h^{2}+3\right)$$

Solution Steps

Factor out 3.

$$3\left(7h^{4}+3h^{2}-3h-7h^{3}\right)$$

Consider 7h^{4}+3h^{2}-3h-7h^{3}. Factor out h.

$$h\left(7h^{3}+3h-3-7h^{2}\right)$$

Consider 7h^{3}+3h-3-7h^{2}. Do the grouping 7h^{3}+3h-3-7h^{2}=\left(7h^{3}+3h\right)+\left(-3-7h^{2}\right), and factor out h in the first and -1 in the second group.

$$h\left(7h^{2}+3\right)-\left(7h^{2}+3\right)$$

Factor out common term 7h^{2}+3 by using distributive property.

$$\left(7h^{2}+3\right)\left(h-1\right)$$

Rewrite the complete factored expression. Polynomial 7h^{2}+3 is not factored since it does not have any rational roots.

$$3h\left(7h^{2}+3\right)\left(h-1\right)$$

Evaluate

$$3h\left(h-1\right)\left(7h^{2}+3\right)$$