Solve -4b^4-500b

$$- 4 b ^ { 4 } - 500 b$$

Factor

$$4b\left(b+5\right)\left(-b^{2}+5b-25\right)$$

Solution Steps

Factor out 4.

$$4\left(-b^{4}-125b\right)$$

Consider -b^{4}-125b. Factor out b.

$$b\left(-b^{3}-125\right)$$

Consider -b^{3}-125. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -125 and q divides the leading coefficient -1. One such root is -5. Factor the polynomial by dividing it by b+5.

$$\left(b+5\right)\left(-b^{2}+5b-25\right)$$

Rewrite the complete factored expression. Polynomial -b^{2}+5b-25 is not factored since it does not have any rational roots.

$$4b\left(b+5\right)\left(-b^{2}+5b-25\right)$$

Evaluate

$$-4b^{4}-500b$$