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The expression \(x^2 + 3x - 28\) can be written as \((x + a)(x - b),\) and the expression \(x^2 - 10x - 56\) written as \((x + 2b)(x + c)\), where \(a\)\(b\), and \(c\) are integers such that \(c > 0.\) What is the value of \(2c-a\)?

tertre  Dec 29, 2017
edited by tertre  Dec 29, 2017
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 #1
avatar+502 
0

I wish I could help u guys but I forgot how to solve these type of questions cuz I used to solve them in grade 9 and 10

Rauhan  Dec 29, 2017
 #2
avatar+5924 
+1

x2 + 3x - 28   =   (x - 4)(x + 7)   =  ( x + (-4) )( x - (-7) )   =   (x + a)(x - b)

 

x2 - 10x - 56   =   (x - 14)(x + 4)   =   ( x + 2(-7) )( x + 4 )   =   (x + 2b)(x + c)

 

So...

a  =  -4  ,   b  =  -7  ,   c  =  4

 

And...

2c - a   =   2(4) - -4   =   8 - -4   =   12

hectictar  Dec 29, 2017

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