Given the equation $x^4 + 2x^3 - 10x^2 - 18x + 9 = 0$, complete the following.
a. List all possible rational roots.
b. Use synthetic division to test several possible rational roots in order to identify one actual root.
c. Use the root from part (b) to solve the equation.
a. List all rational roots that are possible according to the Rational Zero Theorem.
3, -3, 1+\sqrt{2}, 1-\sqrt{2} (Use commas to separate answers as needed.)
b. Use synthetic division to test several possible rational roots in order to identify one actual root.
One rational root of the given equation is ?.
(Simplify your answer.)
c. Use the root from part (b) to solve the equation.
The solution set is ?.
(Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any nu
