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Chapter 0: Problem 34

Factor each trinomial, or state that the trinomial is prime. $$15 x^{2}-19 x+6$$

Short Answer

Expert verified
The trinomial \(15x^{2}-19x+6\) is prime.

Step by step solution

01

Identify the coefficients and constant

Here we have a trinomial in the form \(ax^{2}+bx+c\), where \(a=15\), \(b=-19\), and \(c=6\).
02

Find two numbers

We need to find two numbers which add up to -19, and multiply to \(15 \times 6 = 90\). After some trials, we can observe that these numbers do not exist. Hence, the trinomial cannot be factored using integers.
03

Conclusion

Since we cannot find such numbers, we can conclude that the given trinomial is prime and cannot be factored using integers.

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