Question 1202865
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Constant term: {{{2^5=32}}}<br>
Coefficient of x: {{{(C(5,1)(2^4)(-1))=(5)(16)(-1)=-80}}}<br>
Coefficient of x^2: {{{C(5,2)(2^3)((-1)^2)=(10)(8)(1)=80}}}<br>
In performing the multiplication {{{(k+x)(2-x)^5}}}, the coefficient of x in the product comes from "x" times the constant term in the expansion, plus "k" times the linear term in the expansion. The coefficient of x in the product is<br>
{{{(1)(32)+(k)(-80)=32-80k}}}<br>
Solve to find the value of k for which the linear coefficient in the product is -8:<br>
{{{32-80k=-8}}}
{{{80k=40}}}
{{{k=0.5}}}<br>
ANSWER: k = 0.5<br>