Solve 2x^3+x-1+x^2-3x

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

Factor

$$\left(x-1\right)\left(x+1\right)\left(2x+1\right)$$

Solution Steps

Multiply and combine like terms.

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

Do the grouping 2x^{3}+x^{2}-2x-1=\left(2x^{3}+x^{2}\right)+\left(-2x-1\right), and factor out x^{2} in the first and -1 in the second group.

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

Factor out common term 2x+1 by using distributive property.

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

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression.

$$\left(x-1\right)\left(x+1\right)\left(2x+1\right)$$

Evaluate

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

Solution Steps

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

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