Answer:
p(x) = x³ - ½x² - 5x
Step-by-step explanation:
From the polynomial graph, we can see that the graph curve intersects the x-axis at x = -2, 0 and 2½ or 5/2
And points at which the curve intersects the x-axis means y is zero at that point.
Thus, equation of p is;
p(x) = (x - (-2))(x - 0)(x - 5/2)
p(x) = (x + 2)(x)(x - 5/2)
Expanding, we have;
p(x) = x(x² + 2x - (5/2)x - 5)
p(x) = x(x² - ½x - 5)
p(x) = x³ - ½x² - 5x
