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

Rangcr897 Jul 7, 2024

#2**+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! :)

NotThatSmart Jul 8, 2024