Question 3

We will identify the numerical part of the terms containing $x^2$ and $x^3$.

Step 1 — Identify the polynomial

Let's look at the given polynomial. It is $x^4 - 3x^3 + 6x^2 - 2x + 7$. We need to find specific coefficients.

$P(x) = x^4 - 3x^3 + 6x^2 - 2x + 7$

Step 2 — Find the coefficient of $x^3$

Let's find the term with $x^3$. The term is $-3x^3$. The number multiplying $x^3$ is its coefficient.

$\text{The term containing } x^3 \text{ is } -3x^3$ $\text{The coefficient of } x^3 \text{ is } -3$

$\boxed{\text{Coefficient of } x^3 = -3}$

Step 3 — Find the coefficient of $x^2$

Now, let's find the term with $x^2$. The term is $6x^2$. The number multiplying $x^2$ is its coefficient.

$\text{The term containing } x^2 \text{ is } 6x^2$ $\text{The coefficient of } x^2 \text{ is } 6$

$\boxed{\text{Coefficient of } x^2 = 6}$

Answer

(i) The coefficient of $x^3$ is -3. (ii) The coefficient of $x^2$ is 6.