Solve 55p^2-11p^4+44p^5

$$55 p ^ { 2 } - 11 p ^ { 4 } + 44 p ^ { 5 }$$

Factor

$$11\left(p+1\right)p^{2}\left(4p^{2}-5p+5\right)$$

Solution Steps

Factor out 11.

$$11\left(5p^{2}-p^{4}+4p^{5}\right)$$

Consider 5p^{2}-p^{4}+4p^{5}. Factor out p^{2}.

$$p^{2}\left(5-p^{2}+4p^{3}\right)$$

Consider 5-p^{2}+4p^{3}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 5 and q divides the leading coefficient 4. One such root is -1. Factor the polynomial by dividing it by p+1.

$$\left(p+1\right)\left(4p^{2}-5p+5\right)$$

Rewrite the complete factored expression. Polynomial 4p^{2}-5p+5 is not factored since it does not have any rational roots.

$$11p^{2}\left(p+1\right)\left(4p^{2}-5p+5\right)$$

Evaluate

$$44p^{5}-11p^{4}+55p^{2}$$