When the function f(x) is divided by x-2, the quotient is 3 x^{2}-x+7 and the remainder is -10 . Find the function f(x) and write the result in standard form.

Question

Accepted Answer

Step:1 ：The problem provides that when the function f(x) is divided by x-2, the quotient is 3x^2 - x + 7 and the remainder is -10.Step:2 ：We know from the polynomial division that if a polynomial f(x) is divided by x-a to give a quotient q(x) and a remainder r, then f(x) = (x-a)q(x) + r.Step:3 ：In this case, a=2, q(x) = 3x^2 - x + 7, and r=-10.Step:4 ：We can substitute these values into the formula to find f(x).Step:5 ：So, f(x) = (x-2)(3x^2 - x + 7) - 10.Step:6 ：Simplify the expression to get f(x) = 3x^3 - 7x^2 + 9x - 24.Step:7 ：Final Answer: The function f(x) is (boxed{3x^3 - 7x^2 + 9x - 24}).

Answer

Step: 1 ：The problem provides that when the function f(x) is divided by x-2, the quotient is 3x^2 - x + 7 and the remainder is -10.Step: 2 ：We know from the polynomial division that if a polynomial f(x) is divided by x-a to give a quotient q(x) and a remainder r, then f(x) = (x-a)q(x) + r.Step: 3 ：In this case, a=2, q(x) = 3x^2 - x + 7, and r=-10.Step: 4 ：We can substitute these values into the formula to find f(x).Step: 5 ：So, f(x) = (x-2)(3x^2 - x + 7) - 10.Step: 6 ：Simplify the expression to get f(x) = 3x^3 - 7x^2 + 9x - 24.Step: 7 ：Final Answer: The function f(x) is (boxed{3x^3 - 7x^2 + 9x - 24}).

When the function $f (x)$ is divided by $x - 2$ , the quotient is $3 x^{2} - x + 7$ and the remainder is -10 . Find the function $f (x)$ and write the result in standard form.

Answer

Popular Problems

When the function f(x) is divided by x−2, the quotient is 3x2−x+7 and the remainder is -10 . Find the function f(x) and write the result in standard form.

Answer

Popular Problems

When the function $f (x)$ is divided by $x - 2$ , the quotient is $3 x^{2} - x + 7$ and the remainder is -10 . Find the function $f (x)$ and write the result in standard form.