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Answer
The result of dividing \(3x^{2}-7x+2\) by \(3x-1\) is \(x-2\).
Solution
Calculate or simplify the expression \( (3x^2-7x+2)/(3x-1) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(3x^{2}-7x+2\right)}{\left(3x-1\right)}\)
- step1: Remove the parentheses:
\(\frac{3x^{2}-7x+2}{3x-1}\)
- step2: Factor the expression:
\(\frac{\left(3x-1\right)\left(x-2\right)}{3x-1}\)
- step3: Reduce the fraction:
\(x-2\)
The result of dividing \(3x^{2}-7x+2\) by \(3x-1\) is \(x-2\).
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Simplify this solution The Deep Dive
To divide \( 3x^{2} - 7x + 2 \) by \( 3x - 1 \), you can use polynomial long division. First, divide the leading term of the numerator \( 3x^2 \) by the leading term of the denominator \( 3x \), which gives you \( x \). Then multiply \( x \) by \( 3x - 1 \) to get \( 3x^2 - x \). Subtract this result from the original polynomial: \[ (3x^2 - 7x + 2) - (3x^2 - x) = -6x + 2 \] Next, divide the new leading term \( -6x \) by the leading term \( 3x \), yielding \( -2 \). Multiply \( -2 \) by \( 3x - 1 \) to get \( -6x + 2 \). Subtract again: \[ (-6x + 2) - (-6x + 2) = 0 \] Therefore, the result of the division is: \[ x - 2 \] So, \( \frac{3 x^2 - 7 x + 2}{3 x - 1} = x - 2 \).
