Solve 5m^3+30m^2-35m

$$5 m ^ { 3 } + 30 m ^ { 2 } - 35 m$$

Factor

$$5m\left(m-1\right)\left(m+7\right)$$

Solution Steps

Factor out 5.

$$5\left(m^{3}+6m^{2}-7m\right)$$

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

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

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

$$a+b=6 ab=1\left(-7\right)=-7$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

$$a=-1 b=7$$

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

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

Factor out m in the first and 7 in the second group.

$$m\left(m-1\right)+7\left(m-1\right)$$

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

$$\left(m-1\right)\left(m+7\right)$$

Rewrite the complete factored expression.

$$5m\left(m-1\right)\left(m+7\right)$$

Evaluate

$$5m\left(m-1\right)\left(m+7\right)$$