164k views
1 vote
Which polynomial is prime? • x^2+7 • x^2-25 • 3x^2-27 • 2x^2-8

2 Answers

3 votes

Final Answer:

The prime polynomial is x^2 - 25. Option B is answer.

Step-by-step explanation:

A prime polynomial is a polynomial that cannot be further factored into non-constant and non-trivial polynomials with integer coefficients. Let's analyze each option:

x^2 + 7: This can be factored as (x + √7)(x - √7), making it not prime.

x^2 - 25: This can be factored as (x + 5)(x - 5), but since 5 is a constant integer, it still qualifies as a prime polynomial.

3x^2 - 27: This can be factored as 3(x^2 - 9), which further factors into 3(x + 3)(x - 3). Since 3 is a constant integer, it remains a prime polynomial.

2x^2 - 8: This can be factored as 2(x^2 - 4), which further factors into 2(x + 2)(x - 2). Again, 2 is a constant integer, making it a prime polynomial.

Therefore, the only option that cannot be factored further into non-constant and non-trivial polynomials is x^2 - 25. It remains prime regardless of the constant factor of -1.

Option B is answer.

""

Complete Question

Which polynomial is prime?

x^2+7

x^2-25

3x^2-27

2x^2-8

""

User Zaldy Bughaw
by
6.3k points
1 vote
Explanation

Polynomials can be factored using their zeros and leading coefficient like this:


f(x)=a(x-r_1)(x-r_2)...(x-r_n)

Where a is the leading coefficient and the r's are the zeros of the

User Mrmoment
by
7.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.