To solve the quadratic expression \(x^2 + 7x + 6\), we can factor it.

The factors of this quadratic are numbers that multiply to give \(6\) (the constant term) and add up to \(7\) (the coefficient of \(x\)).

1. Factors of \(6\) are: \(1 \times 6\), and \(2 \times 3\).
2. The pair that adds up to \(7\) is \(1\) and \(6\).

Thus, we can rewrite the expression as:
\[
x^2 + 7x + 6 = (x + 1)(x + 6)
\]

So, the factored form is:
\[
(x + 1)(x + 6)
\]

If you want to find the solutions to the equation \(x^2 + 7x + 6 = 0\), set each factor equal to 0:
\[
x + 1 = 0 \quad \text{or} \quad x + 6 = 0
\]

This gives:
\[
x = -1 \quad \text{or} \quad x = -6
\]

### The solutions are \(x = -1\) and \(x = -6\).

Would you like more details on how factoring works, or do you have any other questions?

Here are 5 related questions to explore:

1. How do you factor more complex quadratic expressions?
2. What are the applications of solving quadratic equations?
3. Can all quadratic equations be factored?
4. What is the quadratic formula, and how is it derived?
5. How do we complete the square for quadratic equations?

**Tip:** When factoring, always check if the quadratic can be factored easily before using more complex methods like the quadratic formula.

Discover how to factor and solve the quadratic equation x^2 + 7x + 6 in this step-by-step guide. Learn about factoring techniques and key algebraic concepts, including the Zero Product Property. Perfect for students in Grades 8-10.

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