Question 1209342
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Let,
f(x) = x^3 + x^2 + x + 1
g(x) = 5x^7 - 3x^4 + 10x^2 - 15


The goal is to find the x^2 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>5x^7</td><td></td><td></td><td></td><td></td></tr><tr><td>-3x^4</td><td></td><td></td><td></td><td></td></tr><tr><td>10x^2</td><td></td><td></td><td></td><td></td></tr><tr><td>-15</td><td></td><td></td><td></td><td></td></tr></table>


To fill out this table, we multiply the headers.
For instance 5x^10 would go in the top left corner (because x^3 times 5x^7 = 5x^10). 
But since 5x^10 isn't an x^2 term, we'll leave this cell blank.


We only fill the cells that have x^2 in them
<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>5x^7</td><td></td><td></td><td></td><td></td></tr><tr><td>-3x^4</td><td></td><td></td><td></td><td></td></tr><tr><td>10x^2</td><td></td><td></td><td></td><td>10x^2</td></tr><tr><td>-15</td><td></td><td>-15x^2</td><td></td><td></td></tr></table>
That would be -15x^2 and 10x^2
They combine to <font color=red>-5</font>x^2


Answer: <font color=red>-5</font>
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