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So this problem, find all integers $n$ such that the quadratic $7x^2 + nx - 11$ can be expressed as the product of two linear factors with integer coefficients.

Hint : Write  $7x^2 + nx - 11 = (Ax + B)(Cx + D).$

So we determined that $n=-76,-4,4,76$ but can you explain how you got this answer like if this was a math paper?

 

 

Thanks in advance, 

MS

coolcoolcool

 Nov 20, 2020
 #1
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Stop trying to cheat on AoPS homework.

 Nov 20, 2020
 #2
avatar+116126 
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Note  that we just need  two things that multiply  to  7  = (7 and 1)

[We could also use -7 and -1, but its not common to use lead negatives in  factoring.....the results would be the same even if we did ]

And we need two  things  that multiply to   -11 = ( 1 and -11)  or  ( 11 and -1))

 

So....we  would have

 

(7x + 1) ( x - 11)

(7x - 1)  (x + 11)

(7x + 11) ( x -1)

(7x - 11) ( x + 1)

 

cool cool cool

 Nov 20, 2020
 #3
avatar+73 
+1

Thanks! 

MathzSolver111  Nov 20, 2020

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