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f(x)=2x^(3)-2x^(2)+18 x-18 The function f is shown. If x-1 is a factor of f, what is the value of f(1) ? Choose 1 answer: (A) -40 (B) -18 (C) 0 (D) 1

f(x)=2x3−2x2+18x−18 f(x)=2 x^{3}-2 x^{2}+18 x-18 \newlineThe function f f is shown. If x−1 x-1 is a factor of f f , what is the value of f(1) f(1) ?\newlineChoose 11 answer:\newline(A) −40-40\newline(B) −18-18\newline(C) 00\newline(D) 11

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Q. f(x)=2x3−2x2+18x−18 f(x)=2 x^{3}-2 x^{2}+18 x-18 \newlineThe function f f is shown. If x−1 x-1 is a factor of f f , what is the value of f(1) f(1) ?\newlineChoose 11 answer:\newline(A) −40-40\newline(B) −18-18\newline(C) 00\newline(D) 11
  1. Given information: We are given that x−1x-1 is a factor of f(x)f(x). According to the Factor Theorem, if x−1x-1 is a factor of f(x)f(x), then f(1)f(1) should be equal to 00.
  2. Calculating f(11): Let's calculate f(11) by substituting x=1x = 1 into the function f(x)=2x3−2x2+18x−18f(x) = 2x^3 - 2x^2 + 18x - 18.\newlinef(1)=2(1)3−2(1)2+18(1)−18f(1) = 2(1)^3 - 2(1)^2 + 18(1) - 18
  3. Performing calculations: Now, perform the calculations:\newlinef(11) = 22(11) - 22(11) + 1818(11) - 1818\newlinef(11) = 22 - 22 + 1818 - 1818
  4. Simplifying the expression: Simplify the expression: f(1)=0f(1) = 0

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