Question 1123580
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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>
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>
The constant term is the product of the constants in the two polynomial factors: (-5)*(-5) = 25<br>
The leading (x^3) coefficient is the product of the leading coefficients of the two factors: (2)*(3) = 6<br>
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>
See if you can find the answer to your problem using this process.<br>
There are two places where the product of one term of each polynomial will produce an x^2 term.
What are those two places?
What are the coefficients of those two products?
The answer to your question is the sum of those two coefficients.