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f(x)=x^(3)-4x^(2)+3x-12 The function f is shown. If x-4 is a factor of f, what is the value of f(4) ? Choose 1 answer: (A) -12 (B) 0 (c) 12 (D) 64

f(x)=x3−4x2+3x−12 f(x)=x^{3}-4 x^{2}+3 x-12 \newlineThe function f f is shown. If x−4 x-4 is a factor of f f , what is the value of f(4)? f(4) ? \newlineChoose 11 answer:\newline(A) −12-12\newline(B) 00\newline(C) 1212\newline(D) 6464

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Q. f(x)=x3−4x2+3x−12 f(x)=x^{3}-4 x^{2}+3 x-12 \newlineThe function f f is shown. If x−4 x-4 is a factor of f f , what is the value of f(4)? f(4) ? \newlineChoose 11 answer:\newline(A) −12-12\newline(B) 00\newline(C) 1212\newline(D) 6464
  1. Calculate f(4)f(4): If x−4x - 4 is a factor of the polynomial f(x)f(x), then by the Factor Theorem, f(4)f(4) should be equal to 00. Let's calculate f(4)f(4) to confirm this.
  2. Substitute x=4x = 4: Substitute x=4x = 4 into the polynomial f(x)=x3−4x2+3x−12f(x) = x^3 - 4x^2 + 3x - 12.\newlinef(4)=(4)3−4⋅(4)2+3⋅(4)−12f(4) = (4)^3 - 4\cdot(4)^2 + 3\cdot(4) - 12
  3. Simplify the expression: Calculate the value of f(4)f(4).f(4)=64−4×16+3×4−12f(4) = 64 - 4\times16 + 3\times4 - 12f(4)=64−64+12−12f(4) = 64 - 64 + 12 - 12
  4. Simplify the expression: Calculate the value of f(4)f(4).f(4)=64−4×16+3×4−12f(4) = 64 - 4 \times 16 + 3 \times 4 - 12f(4)=64−64+12−12f(4) = 64 - 64 + 12 - 12 Simplify the expression.f(4)=0f(4) = 0

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