Chapter 6.5, Problem 3CYU

To determine

To find: the factor of the given polynomial and check whether the polynomial is factored or prime.

Answer to Problem 3CYU

Prime polynomial.

Explanation of Solution

Given:

The given polynomial is $2x^3+5y^3$ .

Calculation:

The given polynomial is $2x^3+5y^3$ .

Since, $\begin{array}{l}2x^3=2{\left(x\right)}^3\\ 5y^3=5{\left(y\right)}^3\end{array}$

Here, the first term and second term of the polynomials are not the perfect cube. Therefore, the polynomial cannot be factorized using the sum of two cubes pattern. It cannot be factored by quadratic methods or GCF methods.

Hence, the given polynomial is prime polynomial.