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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)?

 Oct 2, 2024
 #1
avatar+1238 
+1

 

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

 

 

                                (x3 + x2 + x + 1)(x4 + 3x3 + 8x2 + 7x + 1)    I think you left off that exponent.  

 

                                                          x2 • 1   =   x2     

                                                          x • 7x   =  7x2      

                                                         1 • 8x2  =  8x2     

 

add them up                                                    16x2     

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 Oct 3, 2024
 #2
avatar+24 
+1

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

 Oct 3, 2024

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