https://file.aiquickdraw.com/mathbot/file/173013649367749o3kt0j.jpg

Let's go through the problem step-by-step:

### Part (a): Factorize \( x^2 + 7x + 12 \)
We need to factorize the quadratic expression \( x^2 + 7x + 12 \).

1. **Look for two numbers that multiply to 12 and add up to 7**. These numbers are 3 and 4, since:
   - \( 3 \times 4 = 12 \)
   - \( 3 + 4 = 7 \)

2. **Rewrite the expression as a product of two binomials**:
   \[
   x^2 + 7x + 12 = (x + 3)(x + 4)
   \]

So, the factorization of \( x^2 + 7x + 12 \) is:
\[
(x + 3)(x + 4)
\]

### Part (b): Solve \( x^2 + 7x + 12 = 0 \)
To solve the equation \( x^2 + 7x + 12 = 0 \), we can use the factors we found in part (a).

1. Set each factor equal to zero:
   - \( x + 3 = 0 \) or \( x + 4 = 0 \)

2. Solve for \( x \) in each case:
   - \( x = -3 \)
   - \( x = -4 \)

So, the solutions to the equation \( x^2 + 7x + 12 = 0 \) are:
\[
x = -3 \quad \text{and} \quad x = -4
\]

Would you like more details, or do you have any other questions?

---

### Related Questions to Explore:
1. How can we factorize other quadratic expressions with different coefficients?
2. What if the quadratic expression cannot be factorized easily—how else can we solve it?
3. How does the quadratic formula apply to this problem?
4. Why does factoring work as a method for solving quadratic equations?
5. Can these methods apply to higher-degree polynomials?

### Tip:
When factoring quadratics, look for factor pairs that match both the product and sum conditions for quick factorization.

Factorise x^2 + 7x + 12 and solve x^2 + 7x + 12 = 0.

Learn how to factorize and solve the quadratic equation x^2 + 7x + 12 with a step-by-step guide. This problem covers algebraic methods for factoring and solving quadratic equations, using the zero product property. Ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation