Question

question 5 (5 points)
use pascals triangle to find the coefficient of the third term in the expansion of \\((a + b)^2\\).
a) 4
b) 3
c) 1
d) 2

question 6 (5 points)
determine the \\(y\\)-intercept of the function \\(f(x) = x^4 + 3x^3 - 2x + 7\\).
a) \\((0, 9)\\)
b) \\((0, 7)\\)
c) \\((0, -7)\\)
d) \\((0, 5)\\)

Explanation:

Expand using Pascal's triangle

Using the Pascals Triangle Expansion knowledge point

$$
LATEXBLOCK0
$$

Identify the third term coefficient

Using the Pascals Triangle Expansion knowledge point

$$
LATEXBLOCK1
$$

Find the y-intercept of the function

To find the \(y\)-intercept of \(f(x) = x^4 + 3x^3 - 2x + 7\), we evaluate the function at \(x = 0\).

$$ f(0) = 0^4 + 3(0)^3 - 2(0) + 7 = 7 $$

This corresponds to the coordinate point \((0, 7)\).

Answer:

Question 5

• (A) 4
• (B) 3
• (C) 1 (Correct answer)
• (D) 2

Question 6

• (A) (0, 9)
• (B) (0, 7) (Correct answer)
• (C) (0, -7)
• (D) (0, 5)