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Consider the quadratic expression 13x^2+nx-17 For certain values of n, it may be factored into a product of two linear polynomials, both of which have integer coefficients. What are all such values of n?

 Apr 22, 2022
 #1
avatar+124598 
+1

13 x^2  + nx  - 17

 

We can factor  this  as

 

(13x  + 17) ( x - 1)   so   n  =  17 - 13  =  4

or

(13x - 1) ( x + 17)  so   n =  17*13 - 1 =  220

or

(x - 17) (13x + 1)    so n =  -17(13) + 1 =  -220

or

(x + 1) (13x - 17)    so   n =  -17 + 13  =   -4

 

cool cool cool

 Apr 22, 2022
 #2
avatar+9 
+1

 Thank you!!

 Apr 22, 2022

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