document.write( "Question 1202865: (a). Find the first 3 terms, in ascending powers of x of (2-x)^5.
\n" ); document.write( "(b). Hence find the value of the constant k for which the coefficient of x in the expansion of (k+x)(2-x)^5 is -8 \n" ); document.write( "

Algebra.Com's Answer #838050 by greenestamps(13216) $\"\"$ $\"About$

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\n" ); document.write( "Constant term: $\"2%5E5=32\"$

\n" ); document.write( "Coefficient of x: $\"%28C%285%2C1%29%282%5E4%29%28-1%29%29=%285%29%2816%29%28-1%29=-80\"$

\n" ); document.write( "Coefficient of x^2: $\"C%285%2C2%29%282%5E3%29%28%28-1%29%5E2%29=%2810%29%288%29%281%29=80\"$

\n" ); document.write( "In performing the multiplication $\"%28k%2Bx%29%282-x%29%5E5\"$ , 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

\n" ); document.write( " $\"%281%29%2832%29%2B%28k%29%28-80%29=32-80k\"$

\n" ); document.write( "Solve to find the value of k for which the linear coefficient in the product is -8:

\n" ); document.write( " $\"32-80k=-8\"$
\n" ); document.write( " $\"80k=40\"$
\n" ); document.write( " $\"k=0.5\"$

\n" ); document.write( "ANSWER: k = 0.5

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