Question

1. (0 points) find the 3rd term in the expansion: \\((-2x - 5)^{10}\\)

1. (0 points) find the degree of the polynomial: \\((-3x^3 + 5)^{16}\\)

Explanation:

Step1: Identify the binomial formula

$$T_{k+1} = \binom{n}{k} a^{n-k} b^k$$

Step2: Apply values for 3rd term

$$T_3 = \binom{10}{2} (2x)^{8} (-5)^2$$

Step3: Calculate the 3rd term

$$T_3 = 45 \cdot 256x^8 \cdot 25 = 288000x^8$$

Step4: Find the degree of polynomial

$$\text{Degree} = 3 \times 16 = 48$$

Answer:

1. \(288000x^8\)
2. \(48\)