Solve 12y^6+20y^4-9y^2-15

$$12 y ^ { 6 } + 20 y ^ { 4 } - 9 y ^ { 2 } - 15$$

Factor

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

Solution Steps

Do the grouping 12y^{6}+20y^{4}-9y^{2}-15=\left(12y^{6}+20y^{4}\right)+\left(-9y^{2}-15\right), and factor out 4y^{4} in the first and -3 in the second group.

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

Factor out common term 3y^{2}+5 by using distributive property. The following polynomials are not factored since they do not have any rational roots: 4y^{4}-3,3y^{2}+5.

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

Evaluate

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