Solve 3p^4-5p^2-2

$$3 p ^ { 4 } - 5 p ^ { 2 } - 2$$

Factor

$$\left(p^{2}-2\right)\left(3p^{2}+1\right)$$

Solution Steps

Find one factor of the form kp^{m}+n, where kp^{m} divides the monomial with the highest power 3p^{4} and n divides the constant factor -2. One such factor is 3p^{2}+1. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: p^{2}-2,3p^{2}+1.

$$\left(3p^{2}+1\right)\left(p^{2}-2\right)$$

Evaluate

$$\left(p^{2}-2\right)\left(3p^{2}+1\right)$$