Solve 3x^3+4x^2-7x+1+9x^3-4x^2-6x

$$3 { x }^{ 3 } +4 { x }^{ 2 } -7x+1+9 { x }^{ 3 } -4 { x }^{ 2 } -6x$$

Evaluate

$$12x^{3}-13x+1$$

Solution Steps

Combine 3x^{3} and 9x^{3} to get 12x^{3}.

$$12x^{3}+4x^{2}-7x+1-4x^{2}-6x$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x^{3}-7x+1-6x$$

Combine -7x and -6x to get -13x.

$$12x^{3}-13x+1$$

Factor

$$\left(x-1\right)\left(12x^{2}+12x-1\right)$$

Solution Steps

Multiply and combine like terms.

$$12x^{3}-13x+1$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 1 and q divides the leading coefficient 12. One such root is 1. Factor the polynomial by dividing it by x-1. Polynomial 12x^{2}+12x-1 is not factored since it does not have any rational roots.

$$\left(x-1\right)\left(12x^{2}+12x-1\right)$$