Question 44819
Hello!
In your trinomial
{{{x^2-3x + 7}}}

We have that a = 1, b= -3 and c = 7. The ac test consists of checking whether there are two numbers whose produce is equal to a*c and whose sum is equal to be.

In your case, ac = 1*7 = 7. Since 7 is a prime number, the only pair of numbers whose product is 7 is 1 and 7, or -1 and -7.. In either case, their sum is NOT equal to -3 (1 + 7 = 8  and  -1 + (-7) = -8).

We conclude that this trinomial cannot be factored.


I hope this helps!
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