A polynomial in x has m nonzero terms. Another polynomial in x has n nonzero terms, where m < n. These polynomials are multiplied and all like terms are combined. The resulting polynomial in x has a maximum of how many nonzero terms?

When two polynomials are multiplied, the maximum number of nonzero terms in the resulting polynomial is given by the product of the number of terms in each polynomial.

Step 1: Consider the first polynomial with m nonzero terms. Each of these terms can potentially multiply with each term of the second polynomial.

Step 2: Consider the second polynomial with n nonzero terms. Each of these terms can potentially multiply with each term of the first polynomial.

Step 3: Multiply the number of terms in the first polynomial by the number of terms in the second polynomial. This gives the maximum number of terms in the resulting polynomial before like terms are combined.

So, the maximum number of nonzero terms in the resulting polynomial before like terms are combined is m*n.

Step 4: However, the question specifies that like terms are combined in the resulting polynomial. This means that some terms may be combined to form a single term, reducing the total number of terms.

Therefore, the maximum number of nonzero terms in the resulting polynomial after like terms are combined is min(m,n) + 1. This is because the highest degree term of the resulting polynomial will be the product of the highest degree terms of the two original polynomials, and each lower degree can be obtained by multiplying a term from the first polynomial by a term from the second polynomial, until we reach the constant term (degree 0).

So, the maximum number of nonzero terms in the resulting polynomial after like terms are combined is min(m,n) + 1.