Question 1209342
<pre>

(x<sup>3</sup> + x<sup>2</sup> + x + 1)(5x<sup>7</sup> - 3x<sup>4</sup> + 10x<sup>2</sup> - 15)

We'll get a term in x<sup>2</sup> when we 

A. multiply the term x<sup>2</sup> in the expression on the left by the term
-15 in the expression on the right, getting -15x<sup>2</sup>.

and when we

B. multiply the term 1 in the expression on the left by the 10x<sup>2</sup> in
the expression on the right, getting 10x<sup>2</sup>

That's -15x<sup>2</sup> + 10x<sup>2</sup> = -5x<sup>2</sup>, 

And the coefficient is --- 

     tada! ---

           -5

Edwin</pre>