Solve 3x^3-36x^2+33x

$$3 x ^ { 3 } - 36 x ^ { 2 } + 33 x$$

Factor

$$3x\left(x-11\right)\left(x-1\right)$$

Solution Steps

Factor out 3.

$$3\left(x^{3}-12x^{2}+11x\right)$$

Consider x^{3}-12x^{2}+11x. Factor out x.

$$x\left(x^{2}-12x+11\right)$$

Consider x^{2}-12x+11. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+11. To find a and b, set up a system to be solved.

$$a+b=-12 ab=1\times 11=11$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

$$a=-11 b=-1$$

Rewrite x^{2}-12x+11 as \left(x^{2}-11x\right)+\left(-x+11\right).

$$\left(x^{2}-11x\right)+\left(-x+11\right)$$

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

$$x\left(x-11\right)-\left(x-11\right)$$

Factor out common term x-11 by using distributive property.

$$\left(x-11\right)\left(x-1\right)$$

Rewrite the complete factored expression.

$$3x\left(x-11\right)\left(x-1\right)$$

Evaluate

$$3x\left(x-11\right)\left(x-1\right)$$