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Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

 Jul 7, 2024
 #1
avatar+729 
-1

The value of t is -8.

 Jul 7, 2024
 #2
avatar+1277 
+1

Let's first multiply the terms together and see what we get. 

Multiplying \(x^3(x^2+tx)\), we use the distrbutive property. 

 

Factoring in x^3, we get that

\(x^5+tx^4\)

 

There is no x^2 term in this expansion of the product. 

This means t can pretty much be anything unless it contain x^-2. 

 

Other than that, t could be pretty much any number or polynomial. 

 

Thanks! :)

 Jul 8, 2024

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