Solve 3u^4+24u^2+7u^2+56

$$3 u ^ { 4 } + 24 u ^ { 2 } + 7 u ^ { 2 } + 56$$

Factor

$$\left(3u^{2}+7\right)\left(u^{2}+8\right)$$

Solution Steps

Multiply and combine like terms.

$$3u^{4}+31u^{2}+56$$

Find one factor of the form ku^{m}+n, where ku^{m} divides the monomial with the highest power 3u^{4} and n divides the constant factor 56. One such factor is 3u^{2}+7. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: 3u^{2}+7,u^{2}+8.

$$\left(3u^{2}+7\right)\left(u^{2}+8\right)$$

Evaluate

$$\left(3u^{2}+7\right)\left(u^{2}+8\right)$$

Solution Steps

Combine 24u^{2} and 7u^{2} to get 31u^{2}.

$$3u^{4}+31u^{2}+56$$