Given \( g(x)=-3 x^{5}+7 x^{4}+9 x^{2}-x+9 \), Part 1 of 2 (a) Evaluate \( g(2) \). \( g(2)= \) Part 2 of 2 (b) Determine the remainder when \( g(x) \) is divided by \( (x-2) \). The remainder is

To evaluate \( g(2) \): First, substitute \( x = 2 \) into the function: \[ g(2) = -3(2)^5 + 7(2)^4 + 9(2)^2 - (2) + 9 \] Calculating each term: \[ = -3(32) + 7(16) + 9(4) - 2 + 9 \] \[ = -96 + 112 + 36 - 2 + 9 \] \[ = -96 + 112 = 16 \] \[ 16 + 36 = 52 \] \[ 52 - 2 = 50 \] \[ 50 + 9 = 59 \] So, \( g(2) = 59 \). Now, for the remainder when \( g(x) \) is divided by \( (x-2) \), we can use the Remainder Theorem. According to the theorem, the remainder of \( g(x) \) when divided by \( (x - a) \) is simply \( g(a) \). Since we already calculated \( g(2) \): The remainder is \( 59 \).