Question

Let f(x)=2x2−7x+5
and g(x)=x2+9. Find f/g

Answer 1

To find f/g, perform long division of f(x) by g(x) using the given expressions. The result is f/g = 2 - 7/(x^2 + 9) + (45 - 7x)/(x^2 + 9).

Step-by-step explanation:

To find f/g, we need to divide f(x) by g(x). Substitute the expressions for f(x) and g(x) into the division: (2x^2 - 7x + 5) / (x^2 + 9).

We can use long division to solve this:

1. Divide 2x^2 by x^2, which gives us 2.
2. Multiply (x^2 + 9) by 2, which gives us 2x^2 + 18.
3. Subtract (2x^2 + 18) from (2x^2 - 7x + 5), which gives us -7x - 18.
4. Bring down the next term, which is -7x, and repeat the process.

Continuing the long division, we get:

1. Divide -7x by x^2, which gives us -7.
2. Multiply (x^2 + 9) by -7, which gives us -7x^2 - 63.
3. Subtract (-7x^2 - 63) from (-7x - 18), which gives us 45 - 7x.

The result of the division is: f/g = 2 - 7/(x^2 + 9) + (45 - 7x)/(x^2 + 9).