2𝑥3 + 2𝑥 − 3 = 𝑎(𝑥 + 𝑏)2 + 𝑐 , find 𝑎, 𝑏 and 𝑐.

The equation you provided is a quadratic equation in the form of ax^2 + bx + c = 0. However, the equation you provided is not in this form. To find the values of a, b, and c, we need to rewrite the equation in the standard form.

The equation you provided is: 2x^3 + 2x - 3 = a(x + b)^2 + c

First, we need to expand the right side of the equation:

a(x + b)^2 + c = a(x^2 + 2bx + b^2) + c = ax^2 + 2abx + ab^2 + c

Now, we can compare this with the left side of the equation:

2x^3 + 2x - 3 = ax^2 + 2abx + ab^2 + c

From this, we can see that:

a = 0 (since there is no x^2 term on the left side) 2ab = 2 (from the coefficient of the x term) ab^2 + c = -3 (from the constant term)

Solving these equations will give us the values of a, b, and c. However, since a = 0, this means that b is undefined (since we can't divide by zero), and c can be any real number. Therefore, the equation you provided cannot be written in the form ax^2 + bx + c = 0 with specific values for a, b, and c.