$f(x)=5 x^{4}-12 x^{2}+2 x+k$ is divided by $x-2$, th remainder is 28 , then $k=$
A) -8
B) -36
C) -16
D) 8
E) 16

Answer

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Answer

$\boxed{-8}$

Steps

Step 1 ：According to the Remainder Theorem, if a polynomial f(x) is divided by x - c, then the remainder is f(c). In this case, we are given that the remainder is 28 when f(x) is divided by x - 2. Therefore, we can set up the equation f(2) = 28 and solve for k.

Step 2 ：$f(x) = 5x^4 - 12x^2 + 2x + k$

Step 3 ：$f(2) = 5(2)^4 - 12(2)^2 + 2(2) + k = 28$

Step 4 ：$k + 36 = 28$

Step 5 ：$k = -8$

Step 6 ：$\boxed{-8}$

$f(x)=5 x^{4}-12 x^{2}+2 x+k$ is divided by $x-2$, th remainder is 28 , then $k=$A) -8B) -36C) -16D) 8E) 16

Answer

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$f(x)=5 x^{4}-12 x^{2}+2 x+k$ is divided by $x-2$, th remainder is 28 , then $k=$
A) -8
B) -36
C) -16
D) 8
E) 16