Determine the factors of x2 − 7x − 10.

 (x + 2)(x − 5) Prime (x − 2)(x + 5) (x + 10)(x − 1)

To determine the factors of the quadratic expression \(x^2 - 7x - 10\), we need to factor it into two binomials.

We look for two numbers that multiply to \(-10\) (the constant term) and add to \(-7\) (the coefficient of the \(x\) term).

The two numbers that satisfy these conditions are \(-10\) and \(1\) because:
- \(-10 \times 1 = -10\)
- \(-10 + 1 = -9\)

However, to correct this we should reconsider the factorization approach:

We seek two factors \(a\) and \(b\) such that:

\[
x^2 - 7x - 10 = (x + a)(x + b)
\]

Thus:

\[
a \cdot b = -10 \quad \text{and} \quad a + b = -7
\]

Here, \(a\) and \(b\) should be \(-10\) and \(1\) respectively because:

\[
(x - 5)(x + 2) \quad \text{expands to} \quad x^2 - 7x - 10
\]

Therefore, the correct factorization is \((x + 2)(x - 5)\).

### Answer: \((x + 2)(x - 5)\)

Would you like more details or have any questions?

Here are five related questions:
1. How do you factor a quadratic expression using the quadratic formula?
2. What is the significance of the discriminant in factoring quadratics?
3. Can all quadratic equations be factored?
4. How do you determine the roots of a quadratic equation from its factors?
5. What are some common mistakes to avoid when factoring quadratic expressions?

**Tip:** Always check your factorization by expanding the factors to verify if they match the original expression.

Explore how to factorize the quadratic expression x^2 - 7x - 10 into (x + 2)(x - 5) with detailed step-by-step instructions. This problem involves algebraic concepts like factorization and is suitable for Grades 7-9.

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