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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?

 

pls dont just give me the answer, as i am trying to learn..

 Mar 16, 2023
 #1
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As 23 is a prime number we must have:

 

\((23x+a)(x+b)=23x^2+kx-5\)

 

Multiply out the left-hand side

 

\(23x^2+(a+23b)x+ab=23x^2+kx-5\)

 

Compare coefficients on both sides.

 

Can you take it from here, remembering that the coefficients must be integers.

 Mar 16, 2023
 #2
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"pls dont just give me the answer, as i am trying to learn.."

eh given your title and no effort thats debatable

 Mar 16, 2023

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