The remainder from the division of the algebraic equation is -53/8.
What is the remainder of the algebraic expression?
The remainder of the algebraic expression can be determined by using the long division method.
Given that:
[tex]\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}[/tex]
where:
Using the long division method, we have:
[tex]\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}[/tex]
[tex]\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}[/tex]
Therefore, we can conclude that the remainder is -53/8.
Learn more about the division of algebraic equations here:
https://brainly.com/question/4541471
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