Target Mathematics

1.9: Polynomial remainders, factor theorem and polynomial division

4PM1/2R/June/2022 — Question 4 · 8 marks

f(x)=x3+px2+qx+7,f(x)=x^3+px^2+qx+7,
where pp and qq are integers. (x+1)(x+1) is a factor of f(x)f(x). The remainder when f(x)f(x) is divided by (x+2)(x+2) is −5-5.
(a) Find the value of pp and the value of qq.
(5)
(b) Hence show that f(x)=0f(x)=0 has only one real root.
(3)