SOLUTION: The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is divided by (x-2)the remainder is -6. Show that a=-7

Question 1159544: The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is divided by (x-2)the remainder is -6.
Show that a=-7
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.


According to the Remainder theorem, the fact that the remainder is -6, when f(x) is divided by (x-2), means that f(2) = -6.


In other words,  

    2^3 + 2*2^2 + a*2 - 8 = -6.


It implies

    2a = -6 - 2^3 - 2*2^2 + 8 = -14.


Hence,  a = -14/2 = -7.    ANSWER

Solved.

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   Theorem   (the remainder theorem)
   1. The remainder of division the polynomial    by the binomial    is equal to the value    of the polynomial.
   2. The binomial    divides the polynomial    if and only if the value of    is the root of the polynomial , i.e. .
   3. The binomial    factors the polynomial    if and only if the value of    is the root of the polynomial , i.e. .

See the lessons
    - Divisibility of polynomial f(x) by binomial x-a and the Remainder theorem
    - Solved problems on the Remainder thoerem
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".

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