To rewrite the expression \( 5x^2 - 18 \) in the form \( a(x + b) + c \), we need to factor it or manipulate it into that desired form.

Let's approach it step by step.

### 1. Original expression:
\[
5x^2 - 18
\]

### 2. Rewrite in the form \( a(x + b) + c \):
We want to express it in the form \( a(x + b) + c \), where \( a \), \( b \), and \( c \) are constants. The simplest way to approach this is to try to manipulate the expression into the desired structure by completing the square or factoring out terms.

Since there’s no linear term in \( x \) (no term like \( x \)), we can't factor easily into something like \( (x + b) \). But we can represent the expression as:

\[
5(x^2) + (-18)
\]

Now, it fits the form \( a(x + 0) + (-18) \) where:

- \( a = 5 \)
- \( b = 0 \)
- \( c = -18 \)

Thus, the expression in the form \( a(x + b) + c \) is:
\[
5(x + 0) + (-18)
\]

Or more simply:
\[
5(x + 0) - 18
\]

Would you like more details on other ways of transforming such expressions? Here are some related questions:

1. How do you complete the square for quadratic expressions?
2. What is the process of factoring quadratics?
3. How can we express quadratic functions in vertex form?
4. What is the role of the discriminant in quadratic equations?
5. How does transforming an equation affect its graph?

**Tip**: When rewriting quadratic expressions, completing the square is useful for converting them into vertex form.

Learn how to rewrite the quadratic expression 5x^2 - 18 in the form a(x + b) + c through factoring techniques. This guide explores key algebraic concepts, including factoring out constants and quadratic expressions, suitable for students in Grades 8-10.

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