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Answer :
The expression that is a prime polynomial in the given expression is x^4 + 20x^2 − 100
What are prime polynomials?
It's important to note that prime polynomials are different from prime numbers. Prime numbers are numbers that are divisible only by 1 and themselves, while prime polynomials are polynomials that cannot be factored into the product of two polynomials with integer coefficients.
From the information given:
a) [tex]x^ 3 -27 y^6[/tex]
Since both terms are perfect cubes, factor using the difference of cubes formula,
[tex](x- (3y^2))(x^2+x(3y^2)+(3y^2)^2)[/tex]
[tex](x-3y^2)(x^2+3xy^2+9y^4)[/tex]
b) [tex]x^4 + 20x^2 - 100[/tex] ...The expression is not factorable, hence it is a prime polynomial.
c) [tex]10x^4-5x^3+70x^2+3x[/tex]
[tex]x(10x^3-5x^2+70x+3)[/tex]
Therefore, we conclude that the expression that is a prime polynomial is [tex]x^4 + 20x^2 - 100[/tex]
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