1. The problem involves understanding expressions with $x$, $p(x)$, $x^2$, and $x^2 \times p(x)$.\n\n2. Here, $x$ is a variable, and $p(x)$ typically denotes a function of $x$. For example, $p(x)$ could be a polynomial or any function defined in terms of $x$.\n\n3. $x^2$ means $x$ squared, or $x$ multiplied by itself: $$x^2 = x \times x.$$\n\n4. The expression $x^2 \times p(x)$ means you multiply the function $p(x)$ by $x^2$. If $p(x)$ is a polynomial, say $p(x) = a_n x^n + \dots + a_1 x + a_0$, then multiplying by $x^2$ shifts each term's power up by 2: $$x^2 \times p(x) = a_n x^{n+2} + \dots + a_1 x^3 + a_0 x^2.$$\n\n5. This operation is common in algebra when manipulating polynomials or functions, especially when factoring or expanding expressions.\n\nFinal answer: Understanding $x$, $p(x)$, $x^2$, and $x^2 \times p(x)$ involves recognizing $p(x)$ as a function of $x$ and that multiplying by $x^2$ increases the power of each term in $p(x)$ by 2.