Solve (-3p^3+5p^2-2p)+(-p^3-8p^2-15p)=

$$( - 3 p ^ { 3 } + 5 p ^ { 2 } - 2 p ) + ( - p ^ { 3 } - 8 p ^ { 2 } - 15 p ) =$$

Evaluate

$$-p\left(4p^{2}+3p+17\right)$$

Solution Steps

Combine 5p^{2} and -8p^{2} to get -3p^{2}.

$$-3p^{3}-3p^{2}-2p-p^{3}-15p$$

Combine -2p and -15p to get -17p.

$$-3p^{3}-3p^{2}-17p-p^{3}$$

Combine -3p^{3} and -p^{3} to get -4p^{3}.

$$-4p^{3}-3p^{2}-17p$$

Factor

$$-p\left(4p^{2}+3p+17\right)$$

Solution Steps

Factor out p. Polynomial -4p^{2}-3p-17 is not factored since it does not have any rational roots.

$$p\left(-4p^{2}-3p-17\right)$$