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A student concludes that for all values of x,x^2+x+1 produces a prime number. Which value of x serves as counterexample to prove this conclusion false?

A student concludes that for all values of xx2x1 produces a prime number Which value of x serves as counterexample to prove this conclusion false class=

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Answer:

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Step-by-step explanation:

Substitute the given values into x² + x + 1 and check if result is prime

x = - 4

(- 4)² - 4 + 1 = 16 - 4 + 1 = 13 ← prime

(- 2)² - 2 + 1 = 4 - 2 + 1 = 3 ← prime

(- 3)² - 3 + 1 = 9 - 3 + 1 = 7 ← prime

4² + 4 + 1 = 16 + 4 + 1 = 21 ← not prime

x = 4 serves as a counterexample to disprove this conclusion

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