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.
Learn more about Dividing polynomials