
Which terms complete the factorization of *x*2+27*x*+162 represented by the model?

27, 9*x,* 18*x*

9, 9*x,* 18*x*

27, 9*x,* 27*x*

9, 9*x,* 27*x*

We are asked to factor the quadratic expression \( x^2 + 27x + 162 \) and find which terms match the factorization.

### Step-by-Step Factorization:

The quadratic expression is in the form \( ax^2 + bx + c \), where \( a = 1 \), \( b = 27 \), and \( c = 162 \).

1. We are looking for two numbers that multiply to \( c = 162 \) and add up to \( b = 27 \).

2. Let's find the factors of 162. The pair of factors we are interested in is 9 and 18:
   \[
   9 \times 18 = 162 \quad \text{and} \quad 9 + 18 = 27.
   \]

3. Using these factors, the quadratic can be factored as:
   \[
   (x + 9)(x + 18).
   \]

### Matching the Options:

Given the factorization \( (x + 9)(x + 18) \), we can match the terms provided in the options:

- **First Option**: \( 27, 9x, 18x \) - These do not match the factorization.
- **Second Option**: \( 9, 9x, 18x \) - This corresponds to the factorization \( (x + 9)(x + 18) \). Correct.
- **Third Option**: \( 27, 9x, 27x \) - These do not match the factorization.
- **Fourth Option**: \( 9, 9x, 27x \) - These do not match the factorization.

### Correct Answer:

The correct set of terms that complete the factorization is **9, 9x, 18x**.

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Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general method for factoring quadratic equations?
2. How can you verify if a quadratic equation is factored correctly?
3. What is the difference between factoring and solving a quadratic equation?
4. How can completing the square help in solving quadratic equations?
5. What role do prime factorization and greatest common divisors play in factoring?

**Tip**: Always check that the factors you find multiply back to the original quadratic expression to confirm accuracy.

Which terms complete the factorization of x^2 + 27x + 162 represented by the model? 27, 9x, 18x; 9, 9x, 18x; 27, 9x, 27x; 9, 9x, 27x.

Discover how to factor the quadratic equation x^2 + 27x + 162 with detailed step-by-step instructions. Learn key algebraic concepts such as quadratic trinomials and the zero product property. Suitable for students in Grades 8-10.

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