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Suppose $p(x)$ is a function such that $p(x) + (x^5+3x^3+9x) = (7x^3+24x^2+25x+1)$. Express $p(x)$ as a polynomial with the degrees of the terms in decreasing order.

 Apr 8, 2018

Best Answer 

 #1
avatar+7612 
+3

p(x) + (x5 + 3x3 + 9x)  =  (7x3 + 24x2 + 25x + 1)

 

Subtract  (x5 + 3x3 + 9x)  from both sides of the equation.

 

p(x)  =  (7x3 + 24x2 + 25x + 1)  -  (x5 + 3x3 + 9x)

 

p(x)  =  7x3 + 24x2 + 25x + 1 - x5 - 3x3 - 9x

 

p(x)  =  -x5 + 7x3 - 3x3 + 24x2 + 25x - 9x + 1

 

p(x)  =  -x5 + 4x3 + 24x2 + 16x + 1

 Apr 8, 2018
 #1
avatar+7612 
+3
Best Answer

p(x) + (x5 + 3x3 + 9x)  =  (7x3 + 24x2 + 25x + 1)

 

Subtract  (x5 + 3x3 + 9x)  from both sides of the equation.

 

p(x)  =  (7x3 + 24x2 + 25x + 1)  -  (x5 + 3x3 + 9x)

 

p(x)  =  7x3 + 24x2 + 25x + 1 - x5 - 3x3 - 9x

 

p(x)  =  -x5 + 7x3 - 3x3 + 24x2 + 25x - 9x + 1

 

p(x)  =  -x5 + 4x3 + 24x2 + 16x + 1

hectictar Apr 8, 2018

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