Question 33

Explanation

When divided by $(x - 1)$ the remainder is $3$, meaning

When divided by $(x - 2)$ the remainder is $4$, meaning

Function $f(x)$ divided by $x^2 - 3x + 2 = (x - 1)(x - 2)$ has remainders $f(1)$ and $f(2)$. We can assume, for example, the remainder $s(x) = ax + b$.

We can form equations

When remainder $= f(1)$

When remainder $= f(2)$

Eliminate both equations

The value $a + b = 3$, then $b = 3 - a = 3 - 1 = 2$.

Thus the remainder is