Problem

Use the Remainder Theorem and synthetic division to find each function value. Verify your
g(x)=2x6+2x4x2+5
(a) g(2)=
(b) g(1)=
(c) g(3)=
(d) g(1)=

Answer

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Answer

Final Answer: (a) g(2) = 161, (b) g(1) = 8, (c) g(3) = 1616, (d) g(-1) = 8

Steps

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) = 161, (b) g(1) = 8, (c) g(3) = 1616, (d) g(-1) = 8

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