Show your work neatly Circle your final answer Find the equa

Show your work, neatly. Circle your final answer. Find the equation of the polynomial with the following description Keep in factored form. Degree S. squareroot s of multiplicity 2 at x=3 and x=1. and a squareroot of multiplicity 1 at x=-3. Y intercept (0,-3). What is the leading term and the last tern, tee the following polynomial equation. What is the end behavior? (To the left and to the right)

Solution

1) roots of multiplicity at x = 3 , x = 1 is 2

roots of multiplicity at x = -3 is 1

==> polynomial is P(x) = k(x -(-3)) (x - 3)² (x - 2)²

==> P(x) = k(x + 3)(x - 3)²(x - 2)²

Given that the y - intercept is (0 , -3)

==> -3 = k(0 + 3)(0 - 3)²(0 - 2)²

==> -3 = k(27)(4)

==> k = -3/[(27)(4)] = -1/36

Hence P(x) = (-1/36)(x + 3)(x - 3)²(x - 2)²