Problem 135 - College Algebra

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The trinomial \(x^{2}-4 x-4\) is a prime polynomial.

Step-by-Step Solution

Answer

The statement is true. The trinomial \(x^{2}-4 x-4\) is a prime polynomial as it cannot be factored.

Step 1: Identify the Polynomial

The trinomial provided in the exercise is given by \(x^{2}-4 x-4\).

Step 2: Attempt Factoring the Trinomial

In order to factorize the trinomial \(x^{2}-4x-4\), one should look for two numbers which multiply to -4 and add up to -4. But it seems impossible to find such numbers.

Step 3: Determine if the Trinomial is Prime

Since the trinomial \(x^{2}-4 x-4\) can't be factored, as no such numbers could be found in the previous step, the statement is determined to be true. The trinomial \(x^{2}-4 x-4\) is indeed a prime polynomial.