Question

The polynomial  is denoted by . It is given that  is a factor of , and that  when  is divided by  the remainder is -5. Find the values of  and .

Solution

We are given that;

We are also given that  is a factor of .

When a polynomial, , is divided by , and  is factor of , then the remainder is ZERO i.e. .

We can write factor in standard form as; 

Therefore;

We are also given that when  is divided by  the remainder is -5.

When a polynomial, , is divided by a , the remainder is the constant

We can write divisor in standard form as;

Therefore;

From  we can substitute  in above equation;

Substitution of  in any of these two equations yields value of . We choose;

Hence;