#1**0 **

Solve: ( x^{2} + x + 1 ) ( x^{2} + x + 2 ) = 12

Multiply out: x^{4} + 2x^{3} + 4x^{2} + 3x + 2 = 12

Rewrite: x^{4} + 2x^{3} + 4x^{2} + 3x - 10 = 0

There are two rational solutions; you can find them by trying all the factors of -10:

1, -1, 2, -2, 5, -5, 10, -10 (two of these will work)

After you have these two solutions, you can divide their factors out of the original problem.

This will give you a quadratic that can be solved by using the quadratic equation.

geno3141 Jul 3, 2020