Question

x^2-6x-7
your gonna make me fail so factor good

Answer 1

To factor the quadratic expression \( x^2 - 6x - 7 \), we look for two numbers that multiply to \(-7\) (the constant term) and add to \(-6\) (the coefficient of the linear term).

The two numbers that satisfy these conditions are:
- \( -7 \) and \( 1 \)

Now, we can write the expression as:
\[
x^2 - 7x + 1x - 7
\]

Next, we can group the terms:
\[
(x^2 - 7x) + (1x - 7)
\]

Now, factor by grouping:
\[
x(x - 7) + 1(x - 7)
\]

Combining gives us:
\[
(x + 1)(x - 7)
\]

So, the factored form of \( x^2 - 6x - 7 \) is:
\[
(x - 7)(x + 1)
\]

You can check this factorization by expanding:
\[
(x - 7)(x + 1) = x^2 + x - 7x - 7 = x^2 - 6x - 7
\]

Everything checks out! The correct factorization is:
\[
(x - 7)(x + 1)
\]