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### Theory:

Abraham bar Hiyya Ha-Nasi, also known as Savasorda, was an Arab mathematician famous for his book "Liber Embadorum," published in $$1145 \ AD(CE)$$ and was the first book in Europe present the complete solution to the quadratic equation.
The polynomial is an expression of degree $$n$$ for the variable $$x$$ is of the form $$p(x) = a_0 x^n + a_{1}x^{n-1} + … + a_{n -1}x + a_n$$, where $$a_0, a_1, a_2, …, a_n$$ are coefficients and $$a_0 \ne 0$$.
A quadratic expression is a polynomial of degree $$2$$ for the variable $$x$$ is of the form $$p(x) = ax^2 + bx + c$$, $$a \ne 0$$ and $$a$$, $$b$$ and $$c$$ are real numbers.
Example:
1. Check $$p(x) = (x - 4)^3 + 4x + 2$$ is a quadratic expression.

Solution:

$$p(x) = (x - 4)^3 - 4x + 2$$

$$=$$ $$x^3 - 12x^2 + 48x - 64 - 4x + 2$$ [Using the identity $$(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$$]

$$=$$ $$x^3 - 12x^2 + 44x - 62$$

Here, the degree of the equation is $$3$$.

Thus, the given equation is not a quadratic expression.

2. Check $$p(x) = (x + 2)^3 - x^3 + 3$$ is a quadratic expression.

Solution:

$$p(x) = (x + 2)^3 - x^3 + 3$$

$$=$$ $$x^3 + 6x^2 + 12x + 8 - x^3 + 3$$ [Using the identity $$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$$]

$$=$$ $$6x^2 + 12x - 11$$

Here, the degree of the polynomial is $$2$$.

Thus, the given equation is a quadratic expression.