Question

Use long or synthetic division (x^(2)-3x-20)-:(x-7) Show Your Work

Answer 1

The polynomial x^2 - 3x - 20 divided by x - 7 using long division results in a quotient of x + 4 with no remainder. The process involves dividing terms, multiplying and subtracting from the dividend, and simplifying until all terms are processed.

Step-by-step explanation:

To divide the polynomial x^2 - 3x - 20 by x - 7 using long division, we follow these steps:

1. Write down the dividend and the divisor in long division format.
2. Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient. In this case, x^2 divided by x is x.
3. Multiply the entire divisor by this new term of the quotient and subtract from the current dividend.
4. Bring down the next term from the original dividend and repeat the process until all the terms have been brought down and processed.
5. Eliminate terms wherever possible to simplify the algebra.
6. Write down the remainder, if any.

Carrying out these steps, we find:

• x (x - 7) = x^2 - 7x
• Subtract this from the original dividend to get 4x - 20.
• Divide 4x by x to get +4, and multiply (x - 7) by 4 to subtract from the current dividend.
• No remaining terms are left, so the result is x + 4 with a remainder of 0.

Therefore, the quotient for the division of x^2 - 3x - 20 by x - 7 is x + 4 with no remainder.