Solve -2k-k^3-3k^2

$$- 2 k - k ^ { 3 } - 3 k ^ { 2 }$$

Factor

$$-k\left(k+1\right)\left(k+2\right)$$

Solution Steps

Factor out k.

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

Consider -2-k^{2}-3k. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$-k^{2}-3k-2$$

Factor the expression by grouping. First, the expression needs to be rewritten as -k^{2}+ak+bk-2. To find a and b, set up a system to be solved.

$$a+b=-3 ab=-\left(-2\right)=2$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

$$a=-1 b=-2$$

Rewrite -k^{2}-3k-2 as \left(-k^{2}-k\right)+\left(-2k-2\right).

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

Factor out k in the first and 2 in the second group.

$$k\left(-k-1\right)+2\left(-k-1\right)$$

Factor out common term -k-1 by using distributive property.

$$\left(-k-1\right)\left(k+2\right)$$

Rewrite the complete factored expression.

$$k\left(-k-1\right)\left(k+2\right)$$

Evaluate

$$-k\left(k+1\right)\left(k+2\right)$$