Solve (2x^3-3x^2+5x-1)+(x^2+1-3x)

$$( 2 x ^ { 3 } - 3 x ^ { 2 } + 5 x - 1 ) + ( x ^ { 2 } + 1 - 3 x )$$

Evaluate

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

Solution Steps

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

$$2x^{3}-2x^{2}+5x-1+1-3x$$

Add -1 and 1 to get 0.

$$2x^{3}-2x^{2}+5x-3x$$

Combine 5x and -3x to get 2x.

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor out 2.

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

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

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

Rewrite the complete factored expression. Polynomial x^{2}-x+1 is not factored since it does not have any rational roots.

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