Solve m^3-13m^2+30m

$$m ^ { 3 } - 13 m ^ { 2 } + 30 m$$

Factor

$$m\left(m-10\right)\left(m-3\right)$$

Solution Steps

Factor out m.

$$m\left(m^{2}-13m+30\right)$$

Consider m^{2}-13m+30. Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm+30. To find a and b, set up a system to be solved.

$$a+b=-13 ab=1\times 30=30$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 30.

$$-1,-30 -2,-15 -3,-10 -5,-6$$

Calculate the sum for each pair.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

The solution is the pair that gives sum -13.

$$a=-10 b=-3$$

Rewrite m^{2}-13m+30 as \left(m^{2}-10m\right)+\left(-3m+30\right).

$$\left(m^{2}-10m\right)+\left(-3m+30\right)$$

Factor out m in the first and -3 in the second group.

$$m\left(m-10\right)-3\left(m-10\right)$$

Factor out common term m-10 by using distributive property.

$$\left(m-10\right)\left(m-3\right)$$

Rewrite the complete factored expression.

$$m\left(m-10\right)\left(m-3\right)$$

Evaluate

$$m\left(m-10\right)\left(m-3\right)$$