Solve 1-3x^3-3x^2+6x-1

$$1 - 3 x ^ { 3 } - 3 x ^ { 2 } + 6 x - 1$$

Factor

$$3x\left(1-x\right)\left(x+2\right)$$

Solution Steps

Multiply and combine like terms.

$$-3x^{3}-3x^{2}+6x$$

Factor out 3.

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

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

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

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

$$a+b=-1 ab=-2=-2$$

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

$$a=1 b=-2$$

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

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

Factor out x in the first and 2 in the second group.

$$x\left(-x+1\right)+2\left(-x+1\right)$$

Factor out common term -x+1 by using distributive property.

$$\left(-x+1\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$3x\left(-x+1\right)\left(x+2\right)$$

Evaluate

$$3x\left(1-x\right)\left(x+2\right)$$

Solution Steps

Subtract 1 from 1 to get 0.

$$-3x^{3}-3x^{2}+6x$$