5. f(x) = x ^ 3 + p * x ^ 2 + qx + 6 (a) Find the value of each constants p and q, given that (x - 1) is a factor of f(x) and when f(x) is divided by (x + 1) the remainder is 8. (b) Hence, solve the equation f(x) = 0

Step-by-step explanation:

A polynomial is given to us and we need to find the value of the constants in the given equation . The given polynomial to us is :-

It's mentioned that (x - 1) is a factor of f(x) . This means on putting x = 1 in the given polynomial the value of the polynomial becomes 0 .

Puttting x = 1 in f(x) :-

Now secondly it's given that on dividing the given polynomial by (x + 1) , the remainder is 8 . This means that on putting x = -1 the value of the given polynomial becomes 8 .

Puttting x = (-1) :-

Adding the above two equations :-

Put this value of p in equation (i) .