**Guide :College **

# 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

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 repeatsexampleif you have roots, r1 multiplicity 2 and r2 multiliicty 3 the factors aref(x)=(x-r1)^2(x-r2)^3somultiplicty 2 at x=4multilicty 1 at x=-2(x-4)^2(x-(-2))^1=(x-4)^2(x+2))expandx^3-6x^2+32rememberfor roots, r1 and r2(x-r1)(x-r2)the roots don't change if you multiply whold thing by a unless a=0sothe yint is where x=0so the yint now is 3232 times what=-9.6?divide both sides by 32what=-0.3the polynomial isp(x)=-0.3(x-4)²(x+2)expanded isp(x)=-0.3x³+1.8x²-9.6**...