Solve 4m^3-32m^2+60m

$$4 m ^ { 3 } - 32 m ^ { 2 } + 60 m$$

Factor

$$4m\left(m-5\right)\left(m-3\right)$$

Solution Steps

Factor out 4.

$$4\left(m^{3}-8m^{2}+15m\right)$$

Consider m^{3}-8m^{2}+15m. Factor out m.

$$m\left(m^{2}-8m+15\right)$$

Consider m^{2}-8m+15. Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm+15. To find a and b, set up a system to be solved.

$$a+b=-8 ab=1\times 15=15$$

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 15.

$$-1,-15 -3,-5$$

Calculate the sum for each pair.

$$-1-15=-16 -3-5=-8$$

The solution is the pair that gives sum -8.

$$a=-5 b=-3$$

Rewrite m^{2}-8m+15 as \left(m^{2}-5m\right)+\left(-3m+15\right).

$$\left(m^{2}-5m\right)+\left(-3m+15\right)$$

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

$$m\left(m-5\right)-3\left(m-5\right)$$

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

$$\left(m-5\right)\left(m-3\right)$$

Rewrite the complete factored expression.

$$4m\left(m-5\right)\left(m-3\right)$$

Evaluate

$$4m\left(m-5\right)\left(m-3\right)$$