Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\\9 + 4x^2\\

Explanation:

Identify the given polynomial

We are given the binomial expression:

$$ 9 + 4x^2 $$

Check for a greatest common factor

Using the Factoring Polynomials by GCF knowledge point

$$ \gcd(9, 4) = 1 $$

No common variable or numerical factor exists.

Analyze the binomial structure

Using the Prime Polynomials knowledge point

$$ 9 + 4x^2 = (3)^2 + (2x)^2 $$

This is a sum of two squares. Over the real numbers, a sum of squares with no common factors cannot be factored. Thus, the polynomial is prime.

Answer:

Not Factorable