20
QuizMultiple Choice

Polynomial Operations — Test

Question 20 • Algebra II

What is the fifth term in the binomial expansion of open paren x plus 5 close paren to the 8th power ?

Answer
A
43 comma 750 x to the 4th power
B
175 comma 000 x cubed
C
3 comma 125 x to the 5th power

Explanation

In the binomial expansion of (x + 5)^8, the fifth term uses the exponent 4 on 5 and the exponent 4 on x. Its coefficient is C(8,4) × 5^4 = 70 × 625 = 43,750, so the fifth term is 43,750x^4. This matches choice A.

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