( 18 ) Question is in the photo below **Question 18: Polynomial Division**Given: If \( x - 2 \) divides \( p(x) \) evenly, which statement must be true?- [ ] 2 is the slope of \( p(x) \)- [ ] -2 is the y-intercept of \( p(x) \)- [ ] \( p(2) = 0 \)- [ ] \( p(-2) = 0 \)**Explanation:**To determine which statement is correct, consider the fact that if a polynomial \( p(x) \) is divisible by \( x - 2 \), then \( x = 2 \) is a root of \( p(x) \). This implies that when \( x = 2 \), \( p(2) \) must equal zero. Therefore, the correct option is:- [ ] \( p(2) = 0 \)This is a crucial concept in polynomial algebra, particularly in understanding how roots and factors of polynomials are related. When \( x - a \) is a factor of a polynomial \( p(x) \), it means that \( p(a) = 0 \). Thus, if \( x - 2 \) is a factor, \( p(2) \) must be zero.**Note:** The other options regarding slope and y-intercept are not relevant to determining if \( x - 2 \) divides \( p(x) \) evenly. Also, \( p(-2) = 0 \) corresponds to \( x + 2 \) being a factor, not \( x - 2 \).

Answered: 18. If x - 2 divides p(x) evenly, which…

18. If x - 2 divides p(x) evenly, which statement must be true? O2 is the slope of p(x) O - 2 is the y-intercept of p(x) O p (2)=0 0p(-2) = 0

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,...

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