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eddievic
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Homework Statement
Show by polynomial division that
[tex]\frac{x^3-3x^2+12x-5}{x-2}=(x^2-x+10)+\frac{15}{x-2}[/tex]
The Attempt at a Solution
Please see attachment
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Polynomial division is a method used to divide one polynomial expression by another polynomial expression. It involves breaking down the original expression into smaller, simpler expressions and then finding the quotient and remainder.
To perform polynomial division, you need to follow these steps:
The solution for (x^3-3x^2+12x-5)/(x-2) is x^2-x+2 with a remainder of -1.
To check the solution for polynomial division, you can multiply the quotient by the divisor and add the remainder to the result. The final result should be equal to the original dividend.
Synthetic division is a faster and more efficient method of performing polynomial division, especially when the divisor is a linear expression (in this case, x-2). It involves using the coefficients of the polynomial instead of the full terms, which simplifies the process and reduces the chance of errors.