Solve x^3-23x^3+142x-120

$$x ^ { 3 } - 23 x ^ { 3 } + 142 x - 120$$

Factor

$$2\left(x-1\right)\left(60-11x-11x^{2}\right)$$

Solution Steps

Multiply and combine like terms.

$$-22x^{3}+142x-120$$

Factor out 2.

$$2\left(-11x^{3}+71x-60\right)$$

Consider -11x^{3}+71x-60. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -60 and q divides the leading coefficient -11. One such root is 1. Factor the polynomial by dividing it by x-1.

$$\left(x-1\right)\left(-11x^{2}-11x+60\right)$$

Rewrite the complete factored expression. Polynomial -11x^{2}-11x+60 is not factored since it does not have any rational roots.

$$2\left(x-1\right)\left(-11x^{2}-11x+60\right)$$

Evaluate

$$-22x^{3}+142x-120$$

Solution Steps

Combine x^{3} and -23x^{3} to get -22x^{3}.

$$-22x^{3}+142x-120$$