Solve x^3-3x^2-10x

$$x ^ { 3 } - 3 x ^ { 2 } - 10 x$$

Factor

$$x\left(x-5\right)\left(x+2\right)$$

Solution Steps

Factor out x.

$$x\left(x^{2}-3x-10\right)$$

Consider x^{2}-3x-10. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-10. To find a and b, set up a system to be solved.

$$a+b=-3 ab=1\left(-10\right)=-10$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -10.

$$1,-10 2,-5$$

Calculate the sum for each pair.

$$1-10=-9 2-5=-3$$

The solution is the pair that gives sum -3.

$$a=-5 b=2$$

Rewrite x^{2}-3x-10 as \left(x^{2}-5x\right)+\left(2x-10\right).

$$\left(x^{2}-5x\right)+\left(2x-10\right)$$

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

$$x\left(x-5\right)+2\left(x-5\right)$$

Factor out common term x-5 by using distributive property.

$$\left(x-5\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$x\left(x-5\right)\left(x+2\right)$$

Evaluate

$$x\left(x-5\right)\left(x+2\right)$$