What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

Pythagorearn May 28, 2024

#1**+1 **

I'm going to do this the hard way and expand eveyrhing out.

Expanding the awful polynomial, which I DEFINTELY NOT reccomending, we have

\(x^{7}-7x^{6}+10x^{5}-13x^{4}+8x^{2}-9x+14\).

As you can seem the coefficient is just -9.

If you want to simplify the process, just note this.

In the expansion, the only two terms that matters is 1*-23x amd x*14x. Adding these 2 we get -9.

Thanks! :)

NotThatSmart May 28, 2024

#1**+1 **

Best Answer

I'm going to do this the hard way and expand eveyrhing out.

Expanding the awful polynomial, which I DEFINTELY NOT reccomending, we have

\(x^{7}-7x^{6}+10x^{5}-13x^{4}+8x^{2}-9x+14\).

As you can seem the coefficient is just -9.

If you want to simplify the process, just note this.

In the expansion, the only two terms that matters is 1*-23x amd x*14x. Adding these 2 we get -9.

Thanks! :)

NotThatSmart May 28, 2024