Question: Factor the following if possible.
$x^2 - x - 56$
Select the correct response:
$(x + 8)(x - 7)$
1. **State the problem:** Factor the quadratic expression $$x^2 - x - 56$$.
2. **Recall the factoring formula:** For a quadratic trinomial $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$.
3. Here, $$a = 1$$, $$b = -1$$, and $$c = -56$$.
4. We need two numbers that multiply to $$1 \times (-56) = -56$$ and add to $$-1$$.
5. The pairs of factors of $$-56$$ are:
- $$-8$$ and $$7$$ (sum = $$-1$$)
- $$8$$ and $$-7$$ (sum = $$1$$)
6. The pair $$-8$$ and $$7$$ sums to $$-1$$, which matches $$b$$.
7. Therefore, we can factor as:
$$x^2 - x - 56 = (x - 8)(x + 7)$$.
8. However, the answer choice given is $$(x + 8)(x - 7)$$, which expands to:
$$x^2 - 7x + 8x - 56 = x^2 + x - 56$$, which is not the original expression.
9. So the correct factorization is:
$$\boxed{(x - 8)(x + 7)}$$.
10. **Final answer:** The expression factors as $$(x - 8)(x + 7)$$, not $$(x + 8)(x - 7)$$.