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The expression x^2 + 15x + 54 can be written as (x + a)(x + b), and the expression x^2 - 17x + 72 written as (x - b)(x - c), where a, b, and c are integers. What is the value of a+b+c?

 Sep 23, 2021
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The expression x^2 + 15x + 54 can be written as (x + a)(x + b), and the expression x^2 - 17x + 72 written as (x - b)(x - c), where a, b, and c are integers. What is the value of a+b+c?   

 

x2 + 15x + 54 factors to (x + 6)(x + 9)      a = 6 and b = 9   

 

x2 – 17x + 72 factors to (x – 9)(x – 8)                      b = 9 and c = 8   

 

so a + b + c  =  6 + 9 + 8  =  23   

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 Sep 23, 2021

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