SOLUTION: consider the sum of squares x^2+9.if this sum can be factored, then there are intergers m and n such that x^2+9=(x+m)(x+n). write two equationa relating the sum of m and n to the

Question 114900This question is from textbook McDougal Littell
: consider the sum of squares x^2+9.if this sum can be factored, then there are intergers m and n such that x^2+9=(x+m)(x+n). write two equationa relating the sum of m and n to the coefficients in x^2+9.
show that there are no intergers m and n that satisfy both equations you wrote in part (a). what can you conclude? This question is from textbook McDougal Littell

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
consider the sum of squares x^2+9.if this sum can be factored, then there are integers m and n such that x^2+9=(x+m)(x+n). write two equationa relating the sum of m and n to the coefficients in x^2+9.
mn=9
m+n=0
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show that there are no integers m and n that satisfy both equations you wrote in part
For m+n to equal 0, m would have to be the negative of n
For mn to equal 9 both m and n would have to have the same sign
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(a). what can you conclude?
I'll leave that to you.
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cheers,
Stan H.
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