Suppose sx 2x3 3 Write the indicated expression as a polyno

Suppose

s(x) = 2x³ 3.

Write the indicated expression as a polynomial. (Simplify your answer completely.)

Solution

s(x) = 2x^3 -3

s(x+1) = 2(x+1)^3 -1 = 2[ x^3 +1 +3x^2 +3x ] -3

= 2x^3 + 6x^2 + 6x -1

s(1) = 2 -3 =-1

s(1)/x = -1/x

s(x+1) - s(1)/x

=  2x^3 + 6x^2 + 6x -1 - 1/x

= ( 2x^3 +6x^3 +6x^2 -x - 1)/x