24
QuizMultiple Choice

Polynomial Operations — Test

Question 24 • Algebra II

Which statement about the simplified binomial expansion of open paren A minus b close paren to the n th power , where n is a positive integer, is true?

Answer
A
All terms in the expansion are negative.
B
The first term in the expansion is negative.
C
The first term in the expansion is positive.
D
All terms in the expansion are positive.

Explanation

By the binomial theorem, the first term of (A − b)^n is A^n, which has a positive coefficient. The following term is −nA^(n−1)b, so the signs alternate rather than all being positive or all being negative. Therefore, the true statement is “The first term in the expansion is positive.”

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