Given f(x)=3 x^{2}-6 x+k, and the remainder when f(x) is divided by x-1 is 1 , then what is the value of k ?

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Step:1 ：Given the function (f(x) = 3x^2 - 6x + k), and the remainder when (f(x)) is divided by (x - 1) is 1.Step:2 ：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 have (c = 1) and the remainder is 1.Step:3 ：Set up the equation (f(1) = 1) and solve for (k):Step:4 ：(f(1) = 3(1)^2 - 6(1) + k = 1)Step:5 ：(k - 3 = 1)Step:6 ：(k = 4)Step:7 ：(boxed{k = 4})

Answer

Step: 1 ：Given the function (f(x) = 3x^2 - 6x + k), and the remainder when (f(x)) is divided by (x - 1) is 1.Step: 2 ：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 have (c = 1) and the remainder is 1.Step: 3 ：Set up the equation (f(1) = 1) and solve for (k):Step: 4 ：(f(1) = 3(1)^2 - 6(1) + k = 1)Step: 5 ：(k - 3 = 1)Step: 6 ：(k = 4)Step: 7 ：(boxed{k = 4})

Given $f(x)=3 x^{2}-6 x+k$, and the remainder when $f(x)$ is divided by $x-1$ is 1 , then what is the value of $k$ ?

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