The polynomial of degree 3, P (x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=-2. The y-intercept is y=-9.6

Find a formula for P (x)

Multiplicity is hoa many times it repeats

example

if you have roots, r1 multiplicity 2 and r2 multiliicty 3 the factors are

f (x) = (x-r1) ^2 (x-r2) ^3

so

multiplicty 2 at x=4

multilicty 1 at x=-2

(x-4) ^2 (x - (-2)) ^1=

(x-4) ^2 (x+2))

expand

x^3-6x^2+32

remember

for roots, r1 and r2

(x-r1) (x-r2)

the roots don't change if you multiply whold thing by a unless a=0

so

the yint is where x=0

so the yint now is 32

32 times what=-9.6?

divide both sides by 32

what=-0.3

the polynomial is

p (x) = - 0.3 (x-4) ² (x+2)

expanded is

p (x) = - 0.3x³+1.8x²-9.6