Parthus Connor

2022-07-12

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

determine how many linear factors and zeros the polynomial function has

Mr Solver

To determine the number of linear factors and zeros of the polynomial function $P\left(x\right)={x}^{47}+{x}^{46}$, we need to analyze the polynomial expression.
The polynomial function $P\left(x\right)$ 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 $P\left(x\right)$ 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 $P\left(x\right)$ has at most $47$ zeros.
However, in this particular case, we have a sum of two terms without any common factors. Therefore, the polynomial $P\left(x\right)$ 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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