Solve 3x^3+3x+9-5x^3-7x^2+6-9=

$$3 { x }^{ 3 } +3x+9-5 { x }^{ 3 } -7 { x }^{ 2 } +6-9=$$

Evaluate

$$-\left(x-1\right)\left(2x^{2}+9x+6\right)$$

Solution Steps

Combine 3x^{3} and -5x^{3} to get -2x^{3}.

$$-2x^{3}+3x+9-7x^{2}+6-9$$

Add 9 and 6 to get 15.

$$-2x^{3}+3x+15-7x^{2}-9$$

Subtract 9 from 15 to get 6.

$$-2x^{3}+3x+6-7x^{2}$$

Factor

$$-2\left(x-1\right)\left(x-\frac{-\sqrt{33}-9}{4}\right)\left(x-\frac{\sqrt{33}-9}{4}\right)$$

Solution Steps

Multiply and combine like terms.

$$-2x^{3}-7x^{2}+3x+6$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 6 and q divides the leading coefficient -2. One such root is 1. Factor the polynomial by dividing it by x-1. Polynomial -2x^{2}-9x-6 is not factored since it does not have any rational roots.

$$\left(x-1\right)\left(-2x^{2}-9x-6\right)$$