SOLUTION: (a). Find the first 3 terms, in ascending powers of x of (2-x)^5. (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

Algebra ->  Finance -> SOLUTION: (a). Find the first 3 terms, in ascending powers of x of (2-x)^5. (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      Log On


   

Question 1202865: (a). Find the first 3 terms, in ascending powers of x of (2-x)^5.
(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
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Constant term: 2%5E5=32

Coefficient of x: %28C%285%2C1%29%282%5E4%29%28-1%29%29=%285%29%2816%29%28-1%29=-80

Coefficient of x^2: C%285%2C2%29%282%5E3%29%28%28-1%29%5E2%29=%2810%29%288%29%281%29=80

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

%281%29%2832%29%2B%28k%29%28-80%29=32-80k

Solve to find the value of k for which the linear coefficient in the product is -8:

32-80k=-8
80k=40
k=0.5

ANSWER: k = 0.5