The expression you provided is:

\[
5x^2 - 25x + 30
\]

To factor this expression, follow these steps:

1. **Factor out the greatest common factor (GCF)** from all terms. The GCF here is 5.

\[
5(x^2 - 5x + 6)
\]

2. **Factor the quadratic** inside the parentheses: \( x^2 - 5x + 6 \).

We are looking for two numbers that multiply to \( 6 \) (the constant term) and add to \( -5 \) (the coefficient of \( x \)).

These two numbers are \( -2 \) and \( -3 \), since:

\[
-2 \times -3 = 6 \quad \text{and} \quad -2 + -3 = -5
\]

3. Therefore, we can factor \( x^2 - 5x + 6 \) as \( (x - 2)(x - 3) \).

4. Now, including the GCF, the fully factored form of the original expression is:

\[
5(x - 2)(x - 3)
\]

This is the factored form.

Would you like any more details or have further questions?

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Here are 5 related questions for further exploration:

1. How would you factor \( 6x^2 - 12x + 18 \)?
2. Can you solve the equation \( 5(x - 2)(x - 3) = 0 \)?
3. How do you factor a quadratic expression where the coefficient of \( x^2 \) is greater than 1?
4. What is the general process for factoring a trinomial of the form \( ax^2 + bx + c \)?
5. What are the zeros of the polynomial \( 5x^2 - 25x + 30 \)?

**Tip**: When factoring quadratics, always check if a common factor can be factored out first before proceeding to factor the quadratic.

This guide explains how to factor the quadratic expression 5x^2 - 25x + 30. Follow along with a detailed step-by-step solution, exploring key algebraic concepts such as factoring and quadratic equations. Perfect for students in Grades 7-9.

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