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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)?

 Jun 12, 2024

Best Answer 

 #1
avatar+1252 
+1

There are 2 ways to do the problem. 

 

First, we could take a look at all the possible conbinations we could have to give us x^2. 

 

First off, we have 8x*x = 8x^2. 

Next, we have 7x*x=x^2

Lastly, we have x^2*1 = x^2

 

Adding all the coefficients up, we get \(8+7+1=16\)

 

We could also just factor it, which isn't reccomended, but we get

\(x^{7}+4x^{6}+4x^{5}+19x^{4}+19x^{3}+16x^{2}+16x+1\)

 

Which shows the coefficient of x^2 is 16. 

 

So our final answer is 16

 

Thanks! :)

 Jun 12, 2024
 #1
avatar+1252 
+1
Best Answer

There are 2 ways to do the problem. 

 

First, we could take a look at all the possible conbinations we could have to give us x^2. 

 

First off, we have 8x*x = 8x^2. 

Next, we have 7x*x=x^2

Lastly, we have x^2*1 = x^2

 

Adding all the coefficients up, we get \(8+7+1=16\)

 

We could also just factor it, which isn't reccomended, but we get

\(x^{7}+4x^{6}+4x^{5}+19x^{4}+19x^{3}+16x^{2}+16x+1\)

 

Which shows the coefficient of x^2 is 16. 

 

So our final answer is 16

 

Thanks! :)

NotThatSmart Jun 12, 2024

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