Let g(x) = (x - 1)5(x + 1)6(x - 2)7. What is the multiplicity of the zero x = 1?

Do you mean

g(x) = (x-1)^5*(x+1)^6*(x-2)^7 ?

The multiplicity of the x=1 root is 5.

See http://people.richland.edu/james/lecture/m116/polynomials/polynomials.html
for more details

Assuming those numbers following the factors are exponents, then the exponents are the multiplicities.

(x-1)^3 = (x-1)(x-1)(x-1), so 1 is a root 3 times.

To find the multiplicity of a zero, we need to look at the exponent of that zero in the factored form of the polynomial.

In this case, we are given g(x) = (x - 1)^5(x + 1)^6(x - 2)^7.

The multiplicity of the zero x = 1 is given by the exponent of (x - 1) in the factored form of g(x), which is 5.

Therefore, the multiplicity of the zero x = 1 is 5.