Introduction to quadratic expressions

In the expression $4x^2-3xy+7y-2$, we scan each term to find the one containing the variable $xy$. The term $-3xy$ contains $xy$.

The coefficient is the numerical factor multiplying the variable part. In $-3xy$, the numerical factor is $-3$. The negative sign is part of the coefficient.

The coefficient of $xy$ is $-3$. Remember that the sign belongs to the coefficient — writing just $3$ would be incorrect.

We need to find the coefficient (the number in front) of the variable part $xy$ in the expression $4x^2-3xy+7y-2$.

The value $4$ is the coefficient of $x^2$, not of $xy$. So $4$ is incorrect.

The term is $-3xy$, not $+3xy$. Ignoring the negative sign gives the wrong coefficient. So $3$ is incorrect.

The value $-2$ is a constant term (no variable), not the coefficient of $xy$. So $-2$ is incorrect.

The only remaining option, $-3$, correctly represents the coefficient of $xy$ in the term $-3xy$.

In $24w-w^3=2$, the terms involving $w$ are $24w$ (power 1) and $-w^3$ (power 3). The right side is a constant.

The degree of an equation is the highest exponent of the variable. The highest power of $w$ is $3$, from the term $-w^3$.

Degree 3 → Cubic. The presence of a lower-power term like $24w$ does not change the classification; only the highest power matters.

We must find the highest power of $w$ in $24w-w^3=2$.

A linear equation has degree 1. While $24w$ is a degree-1 term, there is also a degree-3 term $-w^3$. So the equation is not linear.

A quadratic equation has degree 2. There is no $w^2$ term present, and the highest power is 3, so it is not quadratic.

A constant has no variable at all. This equation clearly contains $w$, so it cannot be a constant.

The highest power of $w$ is 3, making this a cubic equation. The answer is Cubic.