3. Which of these statements are always true for the division of a polynomial by a binomial? i) The degree of the remainder is less than that of the divisor. ii) For synthetic division, the variables are removed and only the coefficients are recorded. iii) For synthetic division, the coefficients are listed in ascending order of the powers of the variable. iv) The product of the constant terms of the divisor and the quotient equals the constant term of the diw A. ii and iv C. i and ii D. i, ii, and iii B. i, iii, and iv

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Question
3. Which of these statements are always true for the division of a polynomial by a binomial?
i)
The degree of the remainder is less than that of the divisor.
ii) For synthetic division, the variables are removed and only the coefficients are recorded.
iii) For synthetic division, the coefficients are listed in ascending order of the powers of the variable.
iv) The product of the constant terms of the divisor and the quotient equals the constant term of the divi
A. ii and iv
B. i, i, and iv
C. i and ii
D. i, ii, and i
4. Which integer values of a should be chosen to test for binomial factors of the form x- a of the polynomia
x3 - x2 + 2x + 9?
С. 1, 2, 9
А. -9, -1, 1, 9
В. 1, 3, 9
D. -9,-3,-1, 1, 3, 9
. Which polynomial has x+ 3 as a factor?
С.
x3 - 9x2 + x
A. x3 - 12x2 + 37x
B. x3 - 9x2 - 12x+ 37
D. x3 -9x2 + x + 111
Transcribed Image Text:3. Which of these statements are always true for the division of a polynomial by a binomial? i) The degree of the remainder is less than that of the divisor. ii) For synthetic division, the variables are removed and only the coefficients are recorded. iii) For synthetic division, the coefficients are listed in ascending order of the powers of the variable. iv) The product of the constant terms of the divisor and the quotient equals the constant term of the divi A. ii and iv B. i, i, and iv C. i and ii D. i, ii, and i 4. Which integer values of a should be chosen to test for binomial factors of the form x- a of the polynomia x3 - x2 + 2x + 9? С. 1, 2, 9 А. -9, -1, 1, 9 В. 1, 3, 9 D. -9,-3,-1, 1, 3, 9 . Which polynomial has x+ 3 as a factor? С. x3 - 9x2 + x A. x3 - 12x2 + 37x B. x3 - 9x2 - 12x+ 37 D. x3 -9x2 + x + 111
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