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

 Dec 26, 2023
 #1
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What is the coefficient of x^2 in (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x + 7x + 1)?  

 

                                       Is that 8x a typo that should have been 8x2 ?  

 

To get the product, you have to multiply every term inside the   

first parentheses times every term in the second parentheses.  

 

You could write it like this  

                                                  x3 • (x4 + 3x3 + 15x + 1)       (1)   

plus                                            x2 • (x4 + 3x3 + 15x + 1)       (2)   

plus                                              x • (x4 + 3x3 + 15x + 1)       (3)   

plus                                              1 • (x4 + 3x3 + 15x + 1)       (4)   

 

Let's count up everything that results in an x to the second power.  

 

From (1) there is no x2   

From (2)                                     1 x2    

From (3)                                   15 x2    

From (4) there is no x2    

 

Totalling up the x2 we have 16x2 so the coefficient of the x2 term is 16.  

.

 Dec 26, 2023

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