Solve 2m^3-14m^2+12m

$$2 m ^ { 3 } - 14 m ^ { 2 } + 12 m$$

Factor

$$2m\left(m-6\right)\left(m-1\right)$$

Solution Steps

Factor out 2.

$$2\left(m^{3}-7m^{2}+6m\right)$$

Consider m^{3}-7m^{2}+6m. Factor out m.

$$m\left(m^{2}-7m+6\right)$$

Consider m^{2}-7m+6. Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm+6. To find a and b, set up a system to be solved.

$$a+b=-7 ab=1\times 6=6$$

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 6.

$$-1,-6 -2,-3$$

Calculate the sum for each pair.

$$-1-6=-7 -2-3=-5$$

The solution is the pair that gives sum -7.

$$a=-6 b=-1$$

Rewrite m^{2}-7m+6 as \left(m^{2}-6m\right)+\left(-m+6\right).

$$\left(m^{2}-6m\right)+\left(-m+6\right)$$

Factor out m in the first and -1 in the second group.

$$m\left(m-6\right)-\left(m-6\right)$$

Factor out common term m-6 by using distributive property.

$$\left(m-6\right)\left(m-1\right)$$

Rewrite the complete factored expression.

$$2m\left(m-6\right)\left(m-1\right)$$

Evaluate

$$2m\left(m-6\right)\left(m-1\right)$$