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We are looking to factor \(23x^2 + kx - 5\) Some values of \(k\) allow us to factor it as a product of linear binomials with integer coefficients. What are all such values of k. 

 Aug 8, 2023
 #1
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In order for 23x^2 + kx - 5 to be factorable as a product of linear binomials with integer coefficients, the following conditions must be met:

(1) The coefficient on the x^2 term must be divisible by 2.

(2) The constant term must be divisible by 5.

(3) The coefficient on the x term must be divisible by the product of the other two coefficients.

This means that k must be divisible by 2 and 5, and it must be such that 5 divides 23k - 5. The only values of k that satisfy these conditions are k=−2,−7,−12,−17,−22​.

 Aug 8, 2023
 #2
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 Aug 9, 2023

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