Determine the polynomial Px of least degree whose graph is s

Determine the polynomial P(x) of least degree whose graph is shown in the figure.

Solution

from the graph the roots of the polynomial are -3 , -1 , 1 , 4

General equation of polynomial of least degree is y = k(x + 3)(x + 1)(x - 1)(x - 4)

it passes through the point (2 , -3)

==> -3 = k(2 + 3)(2 + 1)(2 - 1)(2 - 4)

==> -3 = k(5)(3)(1)(-2)

==> k = 1/10

Hence the polynomial is y = (1/10)(x + 3)(x + 1)(x - 1)(x - 4)