3. Given f(x)=3x^2-9x+k, and the remainder when f(x) is divided by x+1 is 14 , then what is the value of k?

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Accepted Answer

Step:1 ：Given the function (f(x)=3x^2-9x+k), and the remainder when (f(x)) is divided by (x+1) is 14.Step:2 ：According to the remainder theorem, the remainder of a polynomial (f(x)) divided by a linear divisor (x-a) is equal to (f(a)). In this case, the divisor is (x+1), so (a=-1).Step:3 ：The remainder when (f(x)) is divided by (x+1) is 14, so (f(-1)=14).Step:4 ：We can substitute (x=-1) into the equation (f(x)=3x^2-9x+k) to find the value of (k).Step:5 ：After substituting, we find that (k=2).Step:6 ：Final Answer: The value of (k) is (boxed{2}).

Answer

Step: 1 ：Given the function (f(x)=3x^2-9x+k), and the remainder when (f(x)) is divided by (x+1) is 14.Step: 2 ：According to the remainder theorem, the remainder of a polynomial (f(x)) divided by a linear divisor (x-a) is equal to (f(a)). In this case, the divisor is (x+1), so (a=-1).Step: 3 ：The remainder when (f(x)) is divided by (x+1) is 14, so (f(-1)=14).Step: 4 ：We can substitute (x=-1) into the equation (f(x)=3x^2-9x+k) to find the value of (k).Step: 5 ：After substituting, we find that (k=2).Step: 6 ：Final Answer: The value of (k) is (boxed{2}).

3. Given f(x)=3x^2-9x+k, and the remainder when f(x) is divided by x+1 is 14 , then what is the value of k?

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