Question: Consider the following polynomial function. f(x) = (x + 3)^2(x - 2)^3(x - 1) Step 1 of 3: Find…

Consider the following polynomial function.

f(x) = (x + 3)^2(x - 2)^3(x - 1)

Step 1 of 3: Find the degree and the y-intercept. Express the intercept as an ordered pair.

Degree:

y-intercept:

Solution

Determine the degree of the polynomial. \[ 2 + 3 + 1 = 6 \] Thus, the degree is 6. Find the y-intercept by evaluating \( f(0) \). \[ f(0) = (0 + 3)^2 (0 - 2)^3 (0 - 1) \] \[ f(0) = 9 \times (-8) \times (-1) = 72 \] Thus, the y-intercept is \( (0, 72) \).