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 remainde is-6. It is also given that f(x) can be written in the form (x+1)(x^2

Algebra ->  Permutations -> 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 remainde is-6. It is also given that f(x) can be written in the form (x+1)(x^2      Log On


   

Question 1159547: 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 remainde is-6.
It is also given that f(x) can be written in the form (x+1)(x^2+bx+c)where b and c are constants.find the values of b and c
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

In two my previous posts   ( see the links 
     
        https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1159544.html
    
    and

        https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1159546.html  )


we studied the given polynomial f(x) = x^3 + 2x^2 + ax - 8  in all details and showed that

under the given conditions the coefficient "a" is -7, so 

    f(x) = x^3 + 2x^2 - 7x - 8.    (1)


Now open the parentheses in the product  (x+1)*(x^2+bx+c)  with unknown coefficients "b" and "c".


Then compare the coefficients at x^2  and x with that in (1).


It will give you the answer.

Solved (in other words, you obtained all necessary instructions from me).