1. Write whether the equation \( (x - 2)^2 = x^2 - 4x + 4 \), where \( a, b, c \) are real numbers and \( a \ne 0 \), can be expressed in the form \( ax^2 + bx + c = 0 \).

2. If the equation \((x+2)^3 = x(x-1)^2\) is expressed in the form of the quadratic equation \(ax^2 + bx + c = 0\) \((a ≠ 0)\), the coefficient of \(x^0\) (the constant term) will be.

(a) -8 (b) -1 (c) 3 (d) 8

3. Write whether the equation \( x + \frac{3}{x} = x^2 \), where \( x \ne 0 \), can be expressed in the form \( ax^2 + bx + c = 0 \), where \( a, b, c \) are real numbers and \( a \ne 0 \).

4. Write whether the equation \( x^2 - 6\sqrt{x} + 2 = 0 \), where \( a, b, c \) are real numbers and \( a \ne 0 \), can be expressed in the form \( ax^2 + bx + c = 0 \).

5. \(\cfrac{x}{4 - x} = \cfrac{1}{3x},\ (x ≠ 0,\ x ≠ 4)\) — Let us express this in the form of a quadratic equation \(ax^2 + bx + c = 0\), where \(a ≠ 0\), and determine the coefficient of \(x\).

6. Let us express \((x + 2)^3 = x(x^2 - 1)\) in the form \(ax^2 + bx + c = 0\), where \(a ≠ 0\), and write down the coefficients of \(x^2\), \(x\), and \(x^0\).

7. Translate: Express \((x + 2)^3 = x(x^2 - 1)\) in the form of a quadratic equation \(ax^2 + bx + c = 0\), where \(a \ne 0\), and write down the coefficients of \(x^2\), \(x\), and \(x^0\) (i.e., the constant term).

8. Let us express \(3x^2 + 7x + 23 = (x + 4)(x + 3) + 2\) in the form of a quadratic equation \(ax^2 + bx + c = 0\), where \(a ≠ 0\).

9. Translate: \(\cfrac{x}{4 - x} = \cfrac{1}{3x}, \ (x \ne 0, \ x \ne 4)\) — If we express this equation in the form of a quadratic equation \(ax^2 + bx + c = 0\) where \(a \ne 0\), then let's determine the coefficient of \(x\).

(a) 1 (b) 2 (c) 3 (d) 4