Solve 5m^3-3m^2-2m

$$5 m ^ { 3 } - 3 m ^ { 2 } - 2 m$$

Factor

$$m\left(m-1\right)\left(5m+2\right)$$

Solution Steps

Factor out m.

$$m\left(5m^{2}-3m-2\right)$$

Consider 5m^{2}-3m-2. Factor the expression by grouping. First, the expression needs to be rewritten as 5m^{2}+am+bm-2. To find a and b, set up a system to be solved.

$$a+b=-3 ab=5\left(-2\right)=-10$$

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 5m^{2}-3m-2 as \left(5m^{2}-5m\right)+\left(2m-2\right).

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

Factor out 5m in the first and 2 in the second group.

$$5m\left(m-1\right)+2\left(m-1\right)$$

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

$$\left(m-1\right)\left(5m+2\right)$$

Rewrite the complete factored expression.

$$m\left(m-1\right)\left(5m+2\right)$$

Evaluate

$$m\left(m-1\right)\left(5m+2\right)$$