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f(x)=x^(4)+4x^(3)-7x^(2)-22 x+24 The function f is shown. If x+3 is a factor of f, what is the value of f(-3) ? Choose 1 answer: (A) -3 (B) 0 (C) 3 (D) 24

f(x)=x4+4x3−7x2−22x+24 f(x)=x^{4}+4 x^{3}-7 x^{2}-22 x+24 \newlineThe function f f is shown. If x+3 x+3 is a factor of f f , what is the value of f(−3) f(-3) ?\newlineChoose 11 answer:\newline(A) −3-3\newline(B) 00\newline(C) 33\newline(D) 2424

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Q. f(x)=x4+4x3−7x2−22x+24 f(x)=x^{4}+4 x^{3}-7 x^{2}-22 x+24 \newlineThe function f f is shown. If x+3 x+3 is a factor of f f , what is the value of f(−3) f(-3) ?\newlineChoose 11 answer:\newline(A) −3-3\newline(B) 00\newline(C) 33\newline(D) 2424
  1. Factor Theorem Application: If x+3x+3 is a factor of f(x)f(x), then by the Factor Theorem, f(−3)f(-3) should be equal to 00. We will substitute x=−3x = -3 into the polynomial to verify this.\newlineCalculation: f(−3)=(−3)4+4∗(−3)3−7∗(−3)2−22∗(−3)+24f(-3) = (-3)^4 + 4*(-3)^3 - 7*(-3)^2 - 22*(-3) + 24\newline=81−108−63+66+24= 81 - 108 - 63 + 66 + 24\newline=81−108−63+90= 81 - 108 - 63 + 90\newline=81−171+90= 81 - 171 + 90\newline=−90+90= -90 + 90\newline$= \(0\)

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