Question

Brittney is factoring the expression 18x2 – 15x + 2. Which expression represents one of the factors?

Group of answer choices

(3x – 2)

(2x – 1)

(9x – 1)

(x – 2)

Answer 1

To determine which expression represents one of the factors of the quadratic expression \(18x^2 - 15x + 2\), we can first use the method of factoring by grouping or by inspection.

Let's look for factors of \(18x^2 - 15x + 2\).

1. **Identify coefficients**:
- The quadratic is in the form \(ax^2 + bx + c\) where \(a = 18\), \(b = -15\), and \(c = 2\).

2. **Check potential factors**:
- We will check the suggested expressions: \(3x - 2\), \(2x - 1\), \(9x - 1\), and \(x - 2\).

3. **Testing \(3x - 2\)**:
\((3x - 2)(6x - 1)\):
- \((3x)(6x) = 18x^2\)
- \((3x)(-1) + (-2)(6x) = -3x - 12x = -15x\)
- \((-2)(-1) = 2\)
- This is a valid factorization, \(3x-2\) is indeed a factor.

4. **Testing \(2x - 1\)**:
For completeness, let’s check \(2x - 1\) and other options as well.
- It might not work directly looking to be a factor since \(18x^2\) would require larger expansions.

5. **Testing \(9x - 1\)**:
\((9x - 1)(2x - 2)\) would lead us away from zero leading or providing outputs that diverge to fit.

6. **Testing \(x - 2\)**:
Those values after calculation do not serve in reaching zero effectively.

Based on the calculations:

**Final Choice**: \((3x - 2)\) is a factor of \(18x^2 - 15x + 2\).

So, the answer is **\(3x - 2\)**.