To factor the quadratic expression \( 5x^2 - 33x + 18 \), we can use factoring by grouping. Here's the process step by step:

### Step 1: Multiply the leading coefficient by the constant term
Multiply \( 5 \) (the coefficient of \( x^2 \)) by \( 18 \) (the constant term):
\[
5 \times 18 = 90
\]
We need to find two numbers that multiply to 90 and add up to -33 (the middle coefficient).

### Step 2: Find two numbers that multiply to 90 and add to -33
The two numbers that satisfy this are \( -30 \) and \( -3 \), because:
\[
-30 \times -3 = 90 \quad \text{and} \quad -30 + -3 = -33
\]

### Step 3: Rewrite the middle term using these two numbers
We can rewrite \( -33x \) as \( -30x - 3x \):
\[
5x^2 - 30x - 3x + 18
\]

### Step 4: Factor by grouping
Group the terms in pairs:
\[
(5x^2 - 30x) - (3x - 18)
\]
Factor out the greatest common factor (GCF) from each group:
\[
5x(x - 6) - 3(x - 6)
\]

### Step 5: Factor out the common binomial factor
Now factor out the common binomial factor \( (x - 6) \):
\[
(5x - 3)(x - 6)
\]

So, the factored form of \( 5x^2 - 33x + 18 \) is:
\[
(5x - 3)(x - 6)
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you factor quadratics when the leading coefficient is not 1?
2. Can you apply factoring by grouping to any quadratic expression?
3. What is the relationship between factoring and solving quadratic equations?
4. How can you verify the factored form by expanding it back?
5. How does factoring relate to finding the roots of a quadratic?

### Tip:
Always check your factored result by expanding it back to the original expression to confirm correctness!

Learn how to factor the quadratic expression 5x^2 - 33x + 18 using the factoring by grouping method. This solution provides a step-by-step explanation, making it perfect for students in Grades 9-10 studying algebra and quadratic equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation