A) Find the remainder when 4x3 - 3x + 5 is divided by 2x - 1.

Here are the solutions to questions 4, 5, 6, 7, 8, and 9.

Question 4:

a) Find the remainder when $4x^3 - 3x + 5$ is divided by $2x - 1$.

Step 1: Use the Remainder Theorem.
Let $P(x) = 4x^3 - 3x + 5$.
To find the remainder when $P(x)$ is divided by $2x-1$, we set $2x-1=0$ and solve for $x$:

$$2x = 1$$ $$x = \frac{1}{2}$$

Step