Solve 14u^4-144u^2+40

$$14 u ^ { 4 } - 144 u ^ { 2 } + 40$$

Factor

$$2\left(7u^{2}-2\right)\left(u^{2}-10\right)$$

Solution Steps

Factor out 2.

$$2\left(7u^{4}-72u^{2}+20\right)$$

Consider 7u^{4}-72u^{2}+20. Find one factor of the form ku^{m}+n, where ku^{m} divides the monomial with the highest power 7u^{4} and n divides the constant factor 20. One such factor is 7u^{2}-2. Factor the polynomial by dividing it by this factor.

$$\left(7u^{2}-2\right)\left(u^{2}-10\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: u^{2}-10,7u^{2}-2.

$$2\left(7u^{2}-2\right)\left(u^{2}-10\right)$$

Evaluate

$$14u^{4}-144u^{2}+40$$