Answer: (x - 1)(x + 1)^2(x - 4)^3
Step-by-step explanation:
First, remember that:
in expressions like: (x - b)^n
b is the value of x where the graph intersects the x-axis.
n can represent:
n = 1, the line just goes through the x-axis
n = 2, the line may change the direction (an inflection point), and touch the x-axis in one point.
n = 3, the line may have two inflection points when it intersects the x-axis.
Then we have the expression:
(x-b)(x-c)^2(x-d)^3
b is in the linear part, the graph crosses the x-axis linearly in x = 1.
c is in the quadratic part, the graph crosses the x-axis with one point of inflection at x = -1.
d is in the cubic part, the graph crosses the x-axis with two inflections in x = 4.
Then we can writhe the polynomial as:
f(x) = (x-1)(x-(-1))^2(x-4)^3 = (x - 1)(x + 1)^2(x - 4)^3
