Explanation Given: The function is f ( x ) = x 5 − 10 x 4 + 20 x 3 − 5 x − 100 . Procedure used: Synthetic Division: Divide the polynomial by x − c : 1. Arrange the polynomial in descending powers, write 0 as coefficient of missing terms in the dividend. 2. Write c for the divisor x − c . 3. Bring down the leading coefficient of the dividend on the bottom row. 4. Multiply c times the value just written on the bottom row. Write the product in the next column in the second row. 5. Add the values in this new column, writing the sum in the bottom row and so on. 6. Use the numbers in the last row to write the quotient. The degree of the quotient is one less than the degree of the dividend. The last number in this row is the remainder”. Calculation: Consider the polynomial function f ( x ) = x 5 − 10 x 4 + 20 x 3 − 5 x − 100 . Find the value of f ( − 10 ) as follows. − 10 1 − 10 20 0 − 5 − 100 − 10 200 − 2200 22 , 000 − 219 , 950 _ 1 − 20 220 − 2200 21 , 995 − 220 , 050 From the above synthetic division, f ( − 10 ) = 220 , 050 . Find the value of f ( 5 )

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Chapter 4.3, Problem 28E

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To find: The functional values f(−10) and f(5) by using synthetic division and check the values by using a graphing calculator.

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Chapter 4.3, Problem 27E

Chapter 4.3, Problem 29E

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The functional values f ( − 10 ) and f ( 5 ) by using synthetic division and check the values by using a graphing calculator.

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To find: The functional values f(−10) and f(5) by using synthetic division and check the values by using a graphing calculator.

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