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When the function f(x) is divided by 2x + 5, the quotient is x² + 2x - 1 and the remainde
is 10. Find the function f(x) and write the result in standard form.

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Final answer:

To find the function f(x), divide the given quotient x² + 2x - 1 by 2x + 5 using long division. Solving the resulting equation provides the value of x, and substituting this value into the original quotient yields the function f(x).


Step-by-step explanation:

To find the function f(x), we can use long division to divide the given quotient x² + 2x - 1 by 2x + 5. Let's start by dividing the first term x² by 2x. The result is (1/2)x.

Next, we multiply the divisor 2x + 5 by the result (1/2)x, which gives us (1/2)x(2x + 5) = x² + (5/2)x.

Now, subtracting this product from the original quotient, we get a remainder of 10. So, (x² + 2x - 1) - (x² + (5/2)x) = 10.

From the above equation, we can solve for x and find that x = -9/4.

Finally, substitute the value of x into the original quotient x² + 2x - 1 to find the value of f(x). So, f(-9/4) = (-9/4)² + 2(-9/4) - 1.


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