Question
Divide. \[ \left(7-20 x+12 x^{2}\right) \div(2 x-1) \] \( \square \)
Ask by Harrington Martinez. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result is \(-7 + 6x\).
Solution
Calculate or simplify the expression \( (7-20*x+12*x^2)/(2*x-1) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(7-20x+12x^{2}\right)}{\left(2x-1\right)}\)
- step1: Remove the parentheses:
\(\frac{7-20x+12x^{2}}{2x-1}\)
- step2: Factor the expression:
\(\frac{\left(2x-1\right)\left(-7+6x\right)}{2x-1}\)
- step3: Reduce the fraction:
\(-7+6x\)
The result of dividing \(7-20x+12x^2\) by \(2x-1\) is \(-7+6x\).
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Simplify this solution Extra Insights
To divide \( (7 - 20x + 12x^2) \) by \( (2x - 1) \), we can use polynomial long division. 1. Arrange the polynomials in standard form: \( 12x^2 - 20x + 7 \). 2. Divide the leading term \( 12x^2 \) by \( 2x \), which gives \( 6x \). 3. Multiply \( 6x \) by \( (2x - 1) \), resulting in \( 12x^2 - 6x \). 4. Subtract this from the original polynomial: \( (12x^2 - 20x + 7) - (12x^2 - 6x) = -14x + 7 \). 5. Next, divide the leading term \( -14x \) by \( 2x \) to get \( -7 \). 6. Multiply \( -7 \) by \( (2x - 1) \), resulting in \( -14x + 7 \). 7. Subtract again: \( (-14x + 7) - (-14x + 7) = 0 \). So, the result of the division is: \[ 6x - 7. \]
