Use the Remainder Theorem and synthetic division to find each function value. Verify your \[ g(x)=2 x^{6}+2 x^{4}-x^{2}+5 \] (a) $g(2)=$ (b) $g(1)=$ (c) $g(3)=$ (d) $g(-1)=$

Step 1 ：The Remainder Theorem states that if a polynomial f(x) is divided by x - k, then the remainder is f(k). In other words, we can find the value of the polynomial at a specific point by substituting that point into the polynomial. In this case, we can find the value of g(x) at x = 2, 1, 3, and -1 by substituting these values into the polynomial.

Step 2 ：Substitute x = 2, 1, 3, and -1 into the polynomial g(x) = 2x^6 + 2x^4 - x^2 + 5.

Step 3 ：The results of substituting x = 2, 1, 3, and -1 into the polynomial g(x) are 161, 8, 1616, and 8 respectively.

Step 4 ：Final Answer: (a) g(2) = \(\boxed{161}\), (b) g(1) = \(\boxed{8}\), (c) g(3) = \(\boxed{1616}\), (d) g(-1) = \(\boxed{8}\)