https://file.aiquickdraw.com/mathbot/file/1726659880389fm9iibm7.jpg

Let's solve the expression \( 5x^2 - 5x - 150 \) by factoring it completely.

### Step 1: Factor out the greatest common factor (GCF)
The GCF of \( 5x^2 \), \( -5x \), and \( -150 \) is 5. We can factor out 5 from the entire expression:
\[
5(x^2 - x - 30)
\]

### Step 2: Factor the quadratic expression inside the parentheses
Now, we need to factor \( x^2 - x - 30 \).

We look for two numbers that multiply to give \( -30 \) (the constant term) and add to give \( -1 \) (the coefficient of the linear term).

The two numbers are \( -6 \) and \( 5 \) because:
\[
-6 \times 5 = -30 \quad \text{and} \quad -6 + 5 = -1
\]

### Step 3: Write the factored form
Now, we can write the factored form of \( x^2 - x - 30 \) as:
\[
(x - 6)(x + 5)
\]

### Step 4: Include the GCF
Don't forget to include the GCF (5) that we factored out earlier. So, the fully factored form of the expression is:
\[
5(x - 6)(x + 5)
\]

### Final Answer:
\[
5x^2 - 5x - 150 = 5(x - 6)(x + 5)
\]

Would you like further clarification or details on any part of this process?

Here are some follow-up questions for practice:
1. How do you find the greatest common factor (GCF) of terms in an expression?
2. What is the relationship between the signs of numbers when factoring a quadratic expression like \(x^2 - x - 30\)?
3. How can you verify that the factored form is correct by expanding?
4. Can every quadratic expression be factored using integers?
5. What method could you use if you couldn't find integer factors for a quadratic expression?

**Tip**: When factoring, always check for a GCF first, as it can simplify the process significantly.

Factor the expression 5x^2 - 5x - 150 completely.

This page explains how to factor the quadratic expression 5x^2 - 5x - 150 completely, covering key algebraic concepts such as factoring, quadratic forms, and finding the greatest common factor (GCF). Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation