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For which value of b can the expression x^2+bx+18 be factored?

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Final answer:

To determine if the expression x² + bx + 18 can be factored, evaluate the discriminant b² - 4ac and check if it is a perfect square.

Step-by-step explanation:

The expression x² + bx + 18 can be factored if and only if its discriminant is a perfect square. The discriminant, represented by the formula b² - 4ac, is the value under the square root in the quadratic formula. In this case, the equation is x² + bx + 18 = 0, so the discriminant is b² - 4ac = b² - 4(1)(18). For the expression to be factored, the discriminant must be a perfect square, meaning it can be written as the square of an integer. So, simplify b² - 4(1)(18), and if it can be written as the square of an integer, the expression can be factored.

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