For Exercises 23–26, consider the division of two polynomials: f ( x ) ÷ ( x − c ) . The result of the synthetic division process is shown here. Write the polynomials representing the a. Dividend. b. Divisor. c. Quotient. d. Remainder. 2 1 − 2 − 25 − 4 − 4 24 4 1 − 6 − 1 0
For Exercises 23–26, consider the division of two polynomials: f ( x ) ÷ ( x − c ) . The result of the synthetic division process is shown here. Write the polynomials representing the a. Dividend. b. Divisor. c. Quotient. d. Remainder. 2 1 − 2 − 25 − 4 − 4 24 4 1 − 6 − 1 0
Solution Summary: The author explains how to determine the polynomial representing the dividend in the result of the synthetic division process.
For Exercises 8–10,
a. Simplify the expression. Do not rationalize the denominator.
b. Find the values of x for which the expression equals zero.
c. Find the values of x for which the denominator is zero.
4x(4x – 5) – 2x² (4)
8.
-6x(6x + 1) – (–3x²)(6)
(6x + 1)2
9.
(4x – 5)?
-
10. V4 – x² - -() 2)
For Exercises 23–24, use the remainder theorem to determine
if the given number c is a zero of the polynomial.
23. f(x) = 3x + 13x + 2x + 52x – 40
a. c = 2
b. c =
24. f(x) = x* + 6x + 9x? + 24x + 20
а. с 3D —5
b. c = 2i
In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x).
18x4 + 9x3 + 3x2 /3x2+1
In Exercises 17–25, divide using synthetic division.
17. (2x2 +x-10)/(x-2)
25. (x2 -5x-5x3 +x4)/(5+x)
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