MAT117Week1DQ2 - as the remainder of division Here order...

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MAT/117 Week1 Discussion Question 2 In your own words, detail the process of polynomial division when the divisor is a monomial. Demonstrate the process with an example. How does this process change when the divisor is not a monomial? Explain in your own words how to evaluate a polynomial for a given value of the variable. Demonstrate the process with an example. Process of polynomial division: The process is same whether the divisor is a monomial or not. The steps for the polynomial division are as follows (assuming the variable of the polynomial is x) 1. Write both the divisor and the dividend in descending order of the exponent of the given variable. For example, if an expression is x^2 - 5 + 2x^3, then rewrite it as 2x^3 + x^2 - 5 2. If the order of the divisor is less than the order of the dividend, then stop. Report the dividend
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Unformatted text preview: as the remainder of division. Here order means the highest power of an expression. For example, the order of 2x^3 + x^2 - 5 is 3 3. Multiply the divisor with a power of x such that the term containing the highest power of x becomes equal in both the divisor and the dividend. 4. Subtract the product obtained by multiplication in step 3 from the dividend. 5. The result of the subtraction in step 4 is the new value of the dividend. Evaluating a polynomial for a given value of the variable: Substitute the value of the variable and evaluate the expression. Example: Let the polynomial be P(x) = x^3 + 2x^2 - 5x + 7 We need to evaluate P(x) at x = 3 Substitute x = 3. We get P(3) = 3^3 + 2 * 3^2 - 5 * 3 + 7 = 27 + 18 - 15 + 7 = 37...
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