Solve b^4-b^3-b+b^2

$$b ^ { 4 } - b ^ { 3 } - b + b ^ { 2 }$$

Factor

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

Solution Steps

Factor out b.

$$b\left(b^{3}-b^{2}-1+b\right)$$

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

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

Factor out common term b-1 by using distributive property.

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

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

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

Evaluate

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