Question 1209341
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The other tutor provides the fastest route. 
My method isn't exactly efficient but I'll discuss it anyway.


f(x) = x^3 + x^2 + x + 1
g(x) = 7x^6 - 3x^5 + 8x - 10
The goal is to find the x coefficient in f(x)*g(x)


I'll use the <a href="https://www.algebra.com/algebra/homework/playground/lessons/box-method.lesson">box method</a>
Place the terms of f(x) along the top.
Place the terms of g(x) along the left side.
<table border = "1" cellpadding = "5"><tr><td></td><td>x^3</td><td>x^2</td><td>x</td><td>1</td></tr><tr><td>7x^6</td><td></td><td></td><td></td><td></td></tr><tr><td>-3x^5</td><td></td><td></td><td></td><td></td></tr><tr><td>8x</td><td></td><td></td><td></td><td></td></tr><tr><td>-10</td><td></td><td></td><td></td><td></td></tr></table>


To fill in each cell, you multiply the headers.
Example: x^3 times 7x^6 = 7x^9 goes in the top left corner.
We could fill this entire table but instead I'll only fill out the cells that have an x term
That would be <font color=blue>-10x</font> and <font color=blue>8x</font> shown below
<table border = "1" cellpadding = "5"><tr><td></td><td>x^3</td><td>x^2</td><td>x</td><td>1</td></tr><tr><td>7x^6</td><td></td><td></td><td></td><td></td></tr><tr><td>-3x^5</td><td></td><td></td><td></td><td></td></tr><tr><td>8x</td><td></td><td></td><td></td><td><font color=blue>8x</font></td></tr><tr><td>-10</td><td></td><td></td><td><font color=blue>-10x</font></td><td></td></tr></table>
Combine like terms to get <font color=red>-2</font>x



Answer: <font color=red>-2</font>
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