Find the zero and multiplicity of f(x)=(x+1)^2(x-2)(x-1)^2(x+2)

Question

Graph, x intercept, y intercept, degree of the polynomial, multiplicity of each x intercept max number of turns.

Answer 1

When f(x)=0, x=-2, -1 (multiplicity=2), 1 (multiplicity=2), 2 so these are the zeroes.

f(0)=-4 (y-intercept), because 1²(-2)(-1)²2=-2×2=-4.

Degree=2+1+2+1=6 (add the exponents or count the zeroes, including their multiplicities).