Solve z/4+4z^4+2z^3

$$\frac { z } { 4 } + 4 z ^ { 4 } + 2 z ^ { 3 }$$

Evaluate

$$4z^{4}+2z^{3}+\frac{z}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4z^{4}+2z^{3} times \frac{4}{4}.

$$\frac{z}{4}+\frac{4\left(4z^{4}+2z^{3}\right)}{4}$$

Since \frac{z}{4} and \frac{4\left(4z^{4}+2z^{3}\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{z+4\left(4z^{4}+2z^{3}\right)}{4}$$

Do the multiplications in z+4\left(4z^{4}+2z^{3}\right).

$$\frac{z+16z^{4}+8z^{3}}{4}$$

Factor

$$\frac{z\left(16z^{3}+8z^{2}+1\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{z+16z^{4}+8z^{3}}{4}$$

Consider z+16z^{4}+8z^{3}. Factor out z.

$$z\left(1+16z^{3}+8z^{2}\right)$$

Rewrite the complete factored expression. Polynomial 1+16z^{3}+8z^{2} is not factored since it does not have any rational roots.

$$\frac{z\left(1+16z^{3}+8z^{2}\right)}{4}$$