(Polynomial reconstruction – linear divisor)
A polynomial f(x) is divided by (x−2) and the quotient obtained is 3x2+4x+1 while the remainder is 5. Given that f(x) is of degree 3, answer the following.
(a) State the relation connecting the dividend, divisor, quotient and remainder obtained on dividing one polynomial by another.
(b) Using the information provided, determine the complete expression for f(x).