Question

Perform the indicated operation. (2u2 - 7) ÷ (u + 3)

Answer 1

To perform the indicated operation (2u² - 7) ÷ (u + 3), use long division to divide the numerator by the denominator step-by-step.

Step-by-step explanation:

To perform the indicated operation (2u² - 7) ÷ (u + 3), we can use long division. Here are the step-by-step instructions:

1. Divide the first term, 2u², by the leading term of the denominator, u. The result is 2u.
2. Multiply the whole denominator, u + 3, by the quotient 2u to get 2u(u + 3), which equals 2u² + 6u.
3. Subtract this product from the numerator, (2u² - 7), to get (-7 - 6u).
4. Bring down the next term from the numerator, which is -7.
5. Divide (-7 - 6u) by the leading term of the denominator, u. The result is -7 + 6, which is -1.
6. Multiply the whole denominator, u + 3, by the quotient -1 to get -u - 3.
7. Subtract this product from the previous result, (-7 - 6u), to get (-6u - u) - 7 - (-3), which equals -7u - 4.
8. Since there are no more terms in the numerator, the final result is (-1 - 7u) divided by (u + 3).