Solve 3x+2x^2-x^3

$$3 x + 2 x ^ { 2 } - x ^ { 3 }$$

Factor

$$-x\left(x-3\right)\left(x+1\right)$$

Solution Steps

Factor out x.

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

Consider 3+2x-x^{2}. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$-x^{2}+2x+3$$

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx+3. To find a and b, set up a system to be solved.

$$a+b=2 ab=-3=-3$$

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.

$$a=3 b=-1$$

Rewrite -x^{2}+2x+3 as \left(-x^{2}+3x\right)+\left(-x+3\right).

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

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

$$-x\left(x-3\right)-\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(-x-1\right)$$

Rewrite the complete factored expression.

$$x\left(x-3\right)\left(-x-1\right)$$

Evaluate

$$-x\left(x-3\right)\left(x+1\right)$$