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

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

Factor

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

Solution Steps

Factor out 5.

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

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

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

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

$$a+b=6 ab=-7=-7$$

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.

$$a=7 b=-1$$

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

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

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

$$-x\left(x-7\right)-\left(x-7\right)$$

Factor out common term x-7 by using distributive property.

$$\left(x-7\right)\left(-x-1\right)$$

Rewrite the complete factored expression.

$$5x\left(x-7\right)\left(-x-1\right)$$

Evaluate

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