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. 3 2 − 5 2 − 4 23 6 3 − 6 − 30 2 1 − 2 − 10 − 1
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. 3 2 − 5 2 − 4 23 6 3 − 6 − 30 2 1 − 2 − 10 − 1
Solution Summary: The author explains the polynomial representing the dividend in the result of the synthetic division process.
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
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)
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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