Question 1206090
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Answers:
<font color=red size=4>quotient = -2x^2+9x-19
remainder = 40</font>


Here's the polynomial long division
*[illustration UploadedScreenshot_25.png]
The expression at the very top is the quotient. The number at the very bottom is the remainder.


And here's what the synthetic division looks like
*[illustration UploadedScreenshot_26.png]
The last number in the bottom row is the remainder.
The other values in the bottom row are the coefficients to the quotient.


Side note: The nonzero remainder indicates that (x+2) is NOT a factor of -2x^3 + 5x^2 - x + 2


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There are many great resources found on the internet that will explain how polynomial long division works.
Here is one such page
<a href="https://www.mathsisfun.com/algebra/polynomials-division-long.html">https://www.mathsisfun.com/algebra/polynomials-division-long.html</a>
Feel free to explore other resources.


Here is a calculator that will provide a step by step look for your particular problem
<a href="https://www.emathhelp.net/en/calculators/algebra-1/polynomial-long-division-calculator/">https://www.emathhelp.net/en/calculators/algebra-1/polynomial-long-division-calculator/</a>


Here is a calculator for synthetic division
<a href="https://www.emathhelp.net/en/calculators/algebra-1/synthetic-division-calculator/">https://www.emathhelp.net/en/calculators/algebra-1/synthetic-division-calculator/</a>
This calculator also explains things step by step.
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