Question 1

The degree of a polynomial is the highest power of its variable.

Step 1 — Degree of $2x^2 - 5x + 3$

Let's look at the polynomial $2x^2 - 5x + 3$. The variable here is $x$. We find the power of $x$ in each term. The powers of $x$ are 2, 1, and 0.

The highest power of $x$ is: $\text{Highest power} = 2$

$\boxed{\text{Degree} = 2}$

Step 2 — Degree of $y^3 + 2y - 1$

Now consider the polynomial $y^3 + 2y - 1$. The variable in this polynomial is $y$. Let's check the power of $y$ in each term. The powers of $y$ are 3, 1, and 0.

The highest power of $y$ is: $\text{Highest power} = 3$

$\boxed{\text{Degree} = 3}$

Step 3 — Degree of $-9$

Next, we have the polynomial $-9$. This is a constant polynomial. A constant polynomial has no variable term with a power greater than zero. We can write $-9$ as $-9x^0$.

The highest power of the variable is: $\text{Highest power} = 0$

$\boxed{\text{Degree} = 0}$

Step 4 — Degree of $4z - 3$

Finally, let's find the degree of $4z - 3$. The variable in this polynomial is $z$. We look at the power of $z$ in each term. The powers of $z$ are 1 and 0.

The highest power of $z$ is: $\text{Highest power} = 1$

$\boxed{\text{Degree} = 1}$

Answer

(i) The degree of $2x^2 - 5x + 3$ is 2. (ii) The degree of $y^3 + 2y - 1$ is 3. (iii) The degree of $-9$ is 0. (iv) The degree of $4z - 3$ is 1.