Solve 2b^4+14b^3-16b

$$2 b ^ { 4 } + 14 b ^ { 3 } - 16 b$$

Factor

$$2b\left(b-1\right)\left(b^{2}+8b+8\right)$$

Solution Steps

Factor out 2.

$$2\left(b^{4}+7b^{3}-8b\right)$$

Consider b^{4}+7b^{3}-8b. Factor out b.

$$b\left(b^{3}+7b^{2}-8\right)$$

Consider b^{3}+7b^{2}-8. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -8 and q divides the leading coefficient 1. One such root is 1. Factor the polynomial by dividing it by b-1.

$$\left(b-1\right)\left(b^{2}+8b+8\right)$$

Rewrite the complete factored expression. Polynomial b^{2}+8b+8 is not factored since it does not have any rational roots.

$$2b\left(b-1\right)\left(b^{2}+8b+8\right)$$

Evaluate

$$2b\left(b^{3}+7b^{2}-8\right)$$