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avatar+534 

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?

 Oct 2, 2024
 #1
avatar+24 
0

Expanding the product, we get \(x^7 + 4x^6 + 4x^5 + 19x^4 + 19x^3 + 16x^2 + 16x + 1\). We see that the coefficient of x is 16.

 Oct 3, 2024
 #4
avatar+37146 
+1

Hello imsmarter1234 ....

   you better check your math on this one !   cheeky

ElectricPavlov  Oct 3, 2024
 #2
avatar+1235 
+1

 

What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 4x^2 + 8x + 7)?     

 

 

                                              (x3 + x2 + x + 1)(x4 + 3x3 + 4x2 + 8x + 7)     x • 7  =   7x       

 

                                              (x3 + x2 + x + 1)(x4 + 3x3 + 4x2 + 8x + 7)     1 • 8x  =  8x       

add them up    

                                                                                                                               15x       

.   

 Oct 3, 2024
 #3
avatar+37146 
+1

The 'x' coefficient will be the result of 

1 * 8x   +  x * 7 =   8x + 7x = 15 x        the coefficient of 'x' will be    15 

 Oct 3, 2024
 #5
avatar+1235 
0

 

Thank you EP for posting the correction.  I posted a correction, too, but mine has been languishing in A.I. Moderation.  It's weird, and infuriating, because I posted an answer to the preceding question, calculated the exact same way, and A.I. did publish that one.     

.   

Bosco  Oct 3, 2024

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