P(x)=x^47+x^46determine how many linear factors and zeros the

Parthus Connor

Parthus Connor

Answered question



determine how many linear factors and zeros the polynomial function has

Answer & Explanation

Mr Solver

Mr Solver

Skilled2023-05-25Added 147 answers

To determine the number of linear factors and zeros of the polynomial function P(x)=x47+x46, we need to analyze the polynomial expression.
The polynomial function P(x) is a sum of two terms, x47 and x46. We can observe that there are no common factors or variables that can be factored out from both terms.
To find the zeros of the polynomial function, we set P(x) equal to zero and solve for x:
To determine the number of zeros, we consider the degree of the polynomial. In this case, the highest power of x is 47. Since a polynomial of degree n can have at most n distinct zeros, we can conclude that the polynomial function P(x) has at most 47 zeros.
However, in this particular case, we have a sum of two terms without any common factors. Therefore, the polynomial P(x) does not factor further into linear factors. This implies that the polynomial has no linear factors and, consequently, no linear zeros.

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