Target Mathematics

1.10: Factors of a polynomial

4PM1/2/June/2021 — Question 6 · 13 marks

f(x)=x3+(p+1)x2−10x+q,f(x)=x^3+(p+1)x^2-10x+q,
where pp and qq are integers.
Given that (x−3)(x-3) is a factor of f(x)f(x),
(a) show that
9p+q+6=0.9p+q+6=0.
(3)
Given that (x+p)(x+p), where p>0p>0, is also a factor of f(x)f(x),
(b) show that
p2+10p+q=0.p^2+10p+q=0.
(3)
(c) Hence find the value of pp and the value of qq.
(5)
(d) Using your values of pp and qq, factorise f(x)f(x) completely.
(2)