x^2+7x+12 Solve byfactorisingthen using the null factor law

To solve the quadratic equation \( x^2 + 7x + 12 = 0 \) by factorizing and using the null factor law, follow these steps:

### Step 1: Factorize the quadratic expression
We need to find two numbers that multiply to give \( 12 \) (the constant term) and add up to give \( 7 \) (the coefficient of \( x \)).

The two numbers are \( 3 \) and \( 4 \), because:
\[
3 \times 4 = 12 \quad \text{and} \quad 3 + 4 = 7
\]

Thus, we can factorize the quadratic expression as:
\[
x^2 + 7x + 12 = (x + 3)(x + 4)
\]

### Step 2: Apply the null factor law
The null factor law states that if the product of two factors is zero, then at least one of the factors must be zero.

So, from \( (x + 3)(x + 4) = 0 \), we have:
\[
x + 3 = 0 \quad \text{or} \quad x + 4 = 0
\]

### Step 3: Solve for \( x \)
Solving each equation:
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]
\[
x + 4 = 0 \quad \Rightarrow \quad x = -4
\]

### Final Answer:
The solutions to the equation are \( x = -3 \) and \( x = -4 \).

Would you like further details or have any questions about these steps?

Here are 5 related questions for practice:
1. Solve \( x^2 + 5x + 6 = 0 \) by factorization and null factor law.
2. Factorize \( x^2 + 8x + 15 = 0 \) and solve.
3. What are the solutions to \( x^2 - 5x + 6 = 0 \)?
4. Solve \( x^2 - 6x + 9 = 0 \) by factorization.
5. How would you solve \( x^2 + 2x - 15 = 0 \)?

**Tip:** Always check if the quadratic equation can be factorized before using other methods like completing the square or the quadratic formula.

x^2 + 7x + 12 Solve by factorizing then using the null factor law

Learn how to solve the quadratic equation x^2 + 7x + 12 by factorizing and applying the null factor law. This step-by-step guide breaks down the solution, covering key algebraic concepts such as factorization and the null factor law. 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