https://file.aiquickdraw.com/mathbot/file/17286534324944o8spsvc.jpg

The expression given is \( 3x^2 - 14x - 49 \), and we are asked to factor it.

### Step-by-Step Factorization:

1. **Identify the terms**: 
   The quadratic expression is \( 3x^2 - 14x - 49 \).
   
2. **Find two numbers that multiply to \( 3 \times (-49) = -147 \) and add up to \( -14 \)**:  
   These numbers are \( -21 \) and \( 7 \) because:
   \[
   -21 \times 7 = -147 \quad \text{and} \quad -21 + 7 = -14
   \]

3. **Split the middle term**:  
   Rewrite the expression as:
   \[
   3x^2 - 21x + 7x - 49
   \]

4. **Factor by grouping**:
   \[
   3x(x - 7) + 7(x - 7)
   \]
   Now, factor out the common binomial:
   \[
   (3x + 7)(x - 7)
   \]

### Conclusion:
The factored form is \( (3x + 7)(x - 7) \), which corresponds to option **D**.

Would you like further details on this process or have any questions?

Here are 5 related questions:
1. How do you solve quadratics using the quadratic formula?
2. Can all quadratics be factored easily like this one?
3. What happens when a quadratic is a perfect square trinomial?
4. How do you use the method of completing the square to solve quadratics?
5. Why is factoring useful in solving quadratic equations?

**Tip**: Always check if the quadratic has a greatest common factor (GCF) before factoring!

What is the factored form of the expression 3x^2 - 14x - 49?

Learn how to factor the quadratic expression 3x^2 - 14x - 49 step-by-step. This problem demonstrates factoring by grouping and key algebraic concepts. Ideal for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation