-2 over 3 x
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x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
x3 + 3x2 - 4x -12 x2(x + 3) - 4(x + 3) (x2 - 4)(x+3)
3X^2 + 9X/3X factor out 3X 3X(X + 3)/3X 3X/3X = 1, so... X + 3 is the simplest form here
Find the remainder when f(x) is divided by (x - k) ƒ(x) = 2x3 + 3x2 + 4x + 18; k = -2 (x - k) = (x - (-2)) = (x + 2) x + 2 = 0 x = -2 By Remainder Theorem ƒ(x) = 2x3 + 3x2 + 4x + 18 ƒ(-2) = 2(-2)3 + 3(-2)2 +4(-2) + 18 = 2(-8) + 3(4) + 4(-2) +18 = -16 + 12 -8 +18 = 6 Thus, the remainder is 6
(3x2 - 6x)/3x = 3x(x-2)/3x = x-2, for x<>0