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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.

 

THX in advance

 Aug 23, 2019
 #1
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also what is the degree of a function???? 

 Aug 23, 2019
 #2
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The degree of a function is the exponent of the leading term. For example: in the polynomial x^2 + 3x + 4, the degree is 2 because it's the exponent of the leading term. 

 Aug 23, 2019
 #3
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THX I understand more now :)

Guest Aug 23, 2019
 #4
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(x^2 + 5x + 6)^2  = 

 

(x^2 +5x + 6) (x^2 + 5x + 6) =

 

     x^4 +5x^3 + 6x^2

+         + 5x^3 +25x^2  + 30x

+                        6x^2 +  30x   + 36

____________________________

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

 

 

And

(px + q) (x^3 + 7x^2 + 3x)  =

 

   px^4  + 7px^3 + 3px^2 

+                qx^3  + 7qx^2 + 3qx

__________________________

  px^4   + (7p+q)x^3 + (3p + 7q)x^2 + 3qx    (2)

 

Combining these  we have

 

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

 

Letting p  = -1   we  can eliminate the x^4  term

 

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

 

(3 + q)x^3 + ( 34 + 7q)x^2 + (60 + 3q)x+ 36

 

Letting q =-3  and we can eliminate the x^3 term

 

(3 + -3)x^3  + (34 + 7(-3) )x^2 + (60 + 3(-3) )x + 36  =

 

13x^2 + 51x + 36    =  degree 2 

 

And p +q =   -1 + (-3)   = -4

 

The degree of a polynomial function[in one variable] is determined  the highest power on that variable

 

 

cool cool cool

 Aug 23, 2019
edited by CPhill  Aug 23, 2019
 #5
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THX FOR ALL THE HELP laugh

 Aug 23, 2019

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