precalculus question

Question

The polynomial of degree , , has a root of multiplicity  at  and a root of multiplicity  at . The -intercept is .Find a formula for 

Answer 1

In factored form your equation is y =a (x-5)^2(x+3). Multiply this out

y=a(x^3-7x^2-5x+75). if the y intercept at -30 you have a point on the function at (0,-30) which you can use to solve for a

-30= a(75)

a=-30/75=-2/5(x-5)^2(x+3)

You can confirm that this is correct by graphing