The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 1 at x=−4. The y-intercept is y=-10; Find a formula for P(x)

Answer 1

Hello Peyton,

The polynomial will have the form P(x) = a*(x-5)(x-5)(x+4)

The y-intercept of P(x) being y=-10 means the graph of the polynomial goes through (0,-10). So you plug (0,-10) to find a:

-10 = a* (0-5)(0-5)(0+4) ---> -10 = a* (-5)(-5)(4) ---> -10 = a*100.

From there all you have to do is:

1. solve for a,
2. In the expression P(x) = a*(x-5)(x-5)(x+4), replace a by the solution you just found.

Cheers.