The function $\mathrm{f}(x) = ax^3 + 4x^2 + bx - 2$, where $a$ and $b$ are constants, is

Question

The function $\mathrm{f}(x) = ax^3 + 4x^2 + bx - 2$, where $a$ and $b$ are constants, is exactly divisible by $x+2$ and leaves a remainder of $4$ when divided by $x+1$. Find the value of $a$ and of $b$.[4] Factorise $f(x)$ completely.[3] By substituting a suitable value of $x$, find the remainder when $3 \ 003 \ 994 \ 998$ is divided by $1002$.[2]

Accepted Answer

(i)a =3, b = -5 (ii)$f(x)=(x+2)(3x+1)(x-1)$ (iii)Remainder = 0

2025 MGS PRELIMS P2 Q10

2025 MGS PRELIMS P2 Q10