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 \(18x^2 - 15x + 2\).
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Identify coefficients:
- The quadratic is in the form \(ax^2 + bx + c\) where \(a = 18\), \(b = -15\), and \(c = 2\).
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Check potential factors:
- We will check the suggested expressions: \(3x - 2\), \(2x - 1\), \(9x - 1\), and \(x - 2\).
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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.
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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.
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Testing \(9x - 1\): \((9x - 1)(2x - 2)\) would lead us away from zero leading or providing outputs that diverge to fit.
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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 \(3x - 2\).