Practice Questions – Polynomials

1. The cubic polynomial  f(x) is defined by  f(x)=x3+ax2+14x+a+1
where a is a constant. It is given that  x+2 is a factor of f(x) .
(i) Use the factor theorem to find the value of a and hence factorise  f(x) completely.[5 marks]

(ii) Hence, without using a calculator, solve the equation f(2x)=3f(x) . [4 marks]