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

Question

Mr Solver · Accepted Answer

To determine the number of linear factors and zeros of the polynomial function

P (x) = x^{47} + x^{46}

, we need to analyze the polynomial expression.
The polynomial function

P (x)

is a sum of two terms,

x^{47}

and

x^{46}

. 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

:

x^{47} + x^{46} = 0

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.

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

Answered question

Answer & Explanation

New Questions in Algebra II