Solve k^3+7k^2-44k

$$k ^ { 3 } + 7 k ^ { 2 } - 44 k$$

Factor

$$k\left(k-4\right)\left(k+11\right)$$

Solution Steps

Factor out k.

$$k\left(k^{2}+7k-44\right)$$

Consider k^{2}+7k-44. Factor the expression by grouping. First, the expression needs to be rewritten as k^{2}+ak+bk-44. To find a and b, set up a system to be solved.

$$a+b=7 ab=1\left(-44\right)=-44$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -44.

$$-1,44 -2,22 -4,11$$

Calculate the sum for each pair.

$$-1+44=43 -2+22=20 -4+11=7$$

The solution is the pair that gives sum 7.

$$a=-4 b=11$$

Rewrite k^{2}+7k-44 as \left(k^{2}-4k\right)+\left(11k-44\right).

$$\left(k^{2}-4k\right)+\left(11k-44\right)$$

Factor out k in the first and 11 in the second group.

$$k\left(k-4\right)+11\left(k-4\right)$$

Factor out common term k-4 by using distributive property.

$$\left(k-4\right)\left(k+11\right)$$

Rewrite the complete factored expression.

$$k\left(k-4\right)\left(k+11\right)$$

Evaluate

$$k\left(k-4\right)\left(k+11\right)$$