Chapter 8, Problem 13SGR

To determine

To classify the polynomial as prime polynomial, difference of squares or perfect square trinomial.

Answer to Problem 13SGR

Prime polynomial

Explanation of Solution

Given:

Polynomial: $x^2-25$

Concept used:

Prime polynomial:

A polynomial with integer coefficients that cannot be reduced to a polynomial of a lower degree is a prime polynomial

Difference of squares:

A polynomial is called difference of squares when each term is a perfect square.

Difference of squares is of the form $a^2-b^2=(a+b)(a-b)$

Perfect square trinomial:

A perfect square trinomial is a polynomial with three terms which can be created by multiplying a binomial to itself.

Perfect square trinomial is of the form ${(a+b)}^2=a^2+2ab+b^2$

Calculation:

Consider the given polynomial,

  $\Rightarrow x^2+25$

The given polynomial cannot be reduced to a polynomial of a lower degree.

Hence, it is a prime polynomial.

Conclusion:

Thus, the given polynomial is classified as prime polynomial.