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Graphs of Polynomial Functions

Question 6 • [INMT3] Integrated Math 3 Sem 1 (26-27)

Which of the following terms, when added to the given polynomial, will change the end behavior?y = –2x7 + 5x6 – 24

Answer
A
–x8
B
–3x5
C
5x7
D
1,000
E
–300

Explanation

End behavior is determined by the polynomial’s highest-degree term. The original leading term is −2x⁷, so it has odd degree and a negative leading coefficient. Adding −x⁸ makes the leading term −x⁸, while adding 5x⁷ changes the x⁷ coefficient to −2 + 5 = 3, making the leading term 3x⁷; both changes alter the end behavior. The other choices have lower degree and do not change the leading term.

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