The remainder from the division of the algebraic equation is -53/8.
<h3>What is the remainder of the algebraic expression?</h3>
The remainder of the algebraic expression can be determined by using the long division method.
Given that:
![\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%20%5Cdfrac%7Bx%5E3%20-%206x%5E2%20%2B%203x%20-%201%7D%7B2x-3%7D%7D)
where:
Using the long division method, we have:
![\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D%20%2B%5Cdfrac%7B-%5Cdfrac%7B9x%5E2%7D%7B2%7D%2B3x%20-1%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20%2B%5Cdfrac%7B-%5Cdfrac%7B-15x%7D%7B4%7D-1%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20-%5Cdfrac%7B15%7D%7B8%7D%2B%5Cdfrac%7B-%5Cdfrac%7B53%7D%7B8%7D%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20-%5Cdfrac%7B15%7D%7B8%7D-%5Cdfrac%7B53%20%7D%7B8%282x-3%29%7D%7D)
Therefore, we can conclude that the remainder is -53/8.
Learn more about the division of algebraic equations here:
brainly.com/question/4541471
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Answer:
270 cubic inches
Step-by-step explanation:
first you multiply 9 times 5 which equals 45 and then you multiply 45 by 6 to get 270. (for volume its length times width times height)
Answer:
d) 5/3 x
Step-by-step explanation:
You substitute a for 2c and b for 5d, so your equation will look like this:
c/d - 2c/5d = x
Then you just simplify into x by making c/d into 5c/5d so you have a common denominator.
5c/5d - 2c/5d = x
3c/5d = x
5/3 is your answer
He need to earn 48
Inequality : 80-32=x
The remainder to this question is 42