Chapter 8.7, Problem 4CYU

To determine

To find: That the given polynomial is a difference of squares, if yes then to factor it.

Answer to Problem 4CYU

The polynomial $x^2-16y^3$ cannot be written as the difference of two squares, it cannot be factorized, so it is a prime polynomial.

Explanation of Solution

Given information:

The given polynomial is $x^2-16y^3$ .

Concept used:

The difference of two squares can be factored as $a^2-b^2=\left(a-b\right)\left(a+b\right)$ .

Calculations:

The given polynomial P (say) is $P=x^2-16y^3$ .

The polynomial can be written as $P={\left(x\right)}^2-{\left(4y\right)}^2\times y$ , i.e., not the difference of two squares.

Therefore, the polynomial $P=x^2-16y^3$ cannot be factorized.

Hence, the polynomial $x^2-16y^3$ is a prime polynomial.

Conclusion:

The polynomial $x^2-16y^3$ cannot be written as the difference of two squares, it cannot be factorized, so it is a prime polynomial.