Solve 2P^3-P^2+2P-1

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

Factor

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

Solution Steps

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

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

Factor out common term 2P-1 by using distributive property. Polynomial P^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

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