Solve {l}{6d^3+42d^2}{-18d}{-126}

$$\left. \begin{array} { l } { 6 d ^ { 3 } + 42 d ^ { 2 } } \\ { - 18 d } \\ { - 126 } \end{array} \right.$$

Factor

$$6\left(d+7\right)\left(d^{2}-3\right)$$

Solution Steps

Factor out 6.

$$6\left(d^{3}+7d^{2}-3d-21\right)$$

Consider d^{3}+7d^{2}-3d-21. Do the grouping d^{3}+7d^{2}-3d-21=\left(d^{3}+7d^{2}\right)+\left(-3d-21\right), and factor out d^{2} in the first and -3 in the second group.

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

Factor out common term d+7 by using distributive property.

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

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

$$6\left(d+7\right)\left(d^{2}-3\right)$$

Evaluate

$$6\left(d+7\right)\left(d^{2}-3\right)$$