To factor the quadratic expression \( s^2 - 5s + 6 \), we are looking for two numbers that multiply to give \( 6 \) (the constant term) and add to give \( -5 \) (the coefficient of the middle term).

1. The two numbers that fit this are \( -2 \) and \( -3 \), because:
   - \( -2 \times -3 = 6 \)
   - \( -2 + -3 = -5 \)

So, the factored form of \( s^2 - 5s + 6 \) is:

\[
(s - 2)(s - 3)
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you solve the equation \( s^2 - 5s + 6 = 0 \)?
2. Can you factor \( s^2 + 5s + 6 \)?
3. What is the sum and product of the roots of \( s^2 - 5s + 6 \)?
4. How do you complete the square for \( s^2 - 5s + 6 \)?
5. How would this factorization change if the middle term was positive?

**Tip:** When factoring quadratics, always check if the product and sum of the factors match the constant and linear coefficients!

Learn how to factor the quadratic equation s^2 - 5s + 6. This step-by-step guide explains how to identify the correct factors and covers core algebraic concepts such as factoring quadratic expressions and applying the zero product property. Ideal for students in Grades 8-10.

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