+0  
 
0
545
1
avatar+598 

The polynomial which results from the expansion of $(x^2+5x+6)^2+(px+q)(x^3+7x^2+3x)$ has degree $2$. Find $p+q$.

 Sep 11, 2017
 #1
avatar+96246 
+1

(x^2+5x+6)^2+(px+q)(x^3+7x^2+3x)

 

x^4 + 10 x^3 + 37 x^2 + 60x + 36   +  px^4 + 7px^3 + 3px^2  + qx^3 + 7qx^2 + 3qx

 

( 1 + p)x^4  + (10 + 7p + q) x^3 + (37 + 3p + 7q)x^2 +( 60+ 3q)x + 36

 

If the resulting polynomial is of degree 2, then

 

1 + p   = 0    →  p  = -1

 

And

 

(10 + 7p + q)  = 0   

(10  - 7  + q)  = 0

3 + q  = 0

q  = -3

 

So

 

(x^2+5x+6)^2+(-1x-3)(x^3+7x^2+3x)  =  13 x^2 + 51 x + 36

 

So

 

p + q  =  ( -1 )  +  (- 3)   =  - 4

 

 

 

cool cool cool    

 Sep 11, 2017

38 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.