Question

Find the quotient of x^2-6x-7 and x-7

Answer 1

To find the quotient of \( x^2 - 6x - 7 \) divided by \( x - 7 \), we can use polynomial long division.

1. **Divide the first term**: Divide \( x^2 \) by \( x \) to get \( x \).

2. **Multiply**: Multiply \( x \) by \( x - 7 \):
\[
x(x - 7) = x^2 - 7x
\]

3. **Subtract**: Subtract this from \( x^2 - 6x - 7 \):
\[
(x^2 - 6x - 7) - (x^2 - 7x) = -6x + 7x - 7 = x - 7
\]

4. **Repeat**: Now, divide \( x \) by \( x \) to get \( 1 \).

5. **Multiply**: Multiply \( 1 \) by \( x - 7 \):
\[
1(x - 7) = x - 7
\]

6. **Subtract**: Subtract this from \( x - 7 \):
\[
(x - 7) - (x - 7) = 0
\]

Since we've finished the division with no remainder, the quotient is:

\[
x + 1
\]

Thus, the quotient of \( x^2 - 6x - 7 \) divided by \( x - 7 \) is:

\[
\boxed{x + 1}
\]