Question

question 3 1 pts rennie is trying to determine the value of the 5th term in the 15th row of pascal’s triangle. which of the following could be the binomial that rennie is trying to expand?
(5x + y)^{15+5}
(x + 8)^{15}
(x + b)^5
(5x + 15)^{15−5}

Explanation:

Step1: Recall Binomial Theorem

The binomial expansion of \((a + b)^n\) uses the \(n\)-th row of Pascal’s Triangle. The \(k\)-th term (starting from \(k = 0\)) has a coefficient from the \(n\)-th row, term number \(k+1\).

Step2: Analyze Term and Row

We need the 5th term in the 15th row. For the 5th term, \(k = 4\) (since \(k+1 = 5\)), so the exponent \(n\) of the binomial should be \(15\) (to use the 15th row).

• Option \((5x + y)^{15 + 5}\) has \(n=20\), wrong.
• Option \((x + b)^5\) has \(n = 5\), wrong.
• Option \((5x + 15)^{15 - 5}\) has \(n = 10\), wrong.
• Option \((x + 8)^{15}\) has \(n = 15\), correct (uses 15th row for expansion, and we can find the 5th term).

Answer:

\((x + 8)^{15}\)