document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123580>Question 1123580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the product of the binomial (2x-5) with the trinomial (3x^2+2x-5) is formed, what is the coefficient of the x^2 term? Please help me answer this.  </SPAN>\n" );
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document.write( "It wouldn't take much work to perform the entire polynomial multiplication; however, there are times when it is a useful skill to be able to determine the coefficient of a particular power in the product of two (or more) binomials, without performing the entire multiplication.<br><BR>\n" );
document.write( "To do this, you need to think about where terms of particular powers in the product come from in the multiplication.  In this product....<br><BR>\n" );
document.write( "The constant term is the product of the constants in the two polynomial factors: (-5)*(-5) = 25<br><BR>\n" );
document.write( "The leading (x^3) coefficient is the product of the leading coefficients of the two factors: (2)*(3) = 6<br><BR>\n" );
document.write( "The coefficient of the x term in the product comes from two places -- the product of the x term in the first polynomial and the constant in the second; and the product of the constant in the first polynomial and the x term in the other: (2)(-5)+(-5)(2) = -20<br><BR>\n" );
document.write( "See if you can find the answer to your problem using this process.<br><BR>\n" );
document.write( "There are two places where the product of one term of each polynomial will produce an x^2 term.<BR>\n" );
document.write( "What are those two places?<BR>\n" );
document.write( "What are the coefficients of those two products?<BR>\n" );
document.write( "The answer to your question is the sum of those two coefficients. </SPAN>\n" );
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