Question

Which of the following is a correct factorization of \(72 x^{2}-24 x+2 ?\) (A) \(-9(3 x-1)^{2}\) (B) \(8\left(9 x-\frac{1}{2}\right)^{2}\) (C) \(8\left(3 x-\frac{1}{2}\right)\left(3 x-\frac{1}{2}\right)\) (D) \(-8\left(3 x-\frac{1}{2}\right)^{2}\)

Short answer

The correct factorization for \(72 x^{2}-24 x+2\) is option (C), which is \(8(3x - 1/2)(3x - 1/2)\).

Step-by-step solution

Expand all options (A, B, C, and D)

A) If you expand \(-9(3x - 1)^2\), it results in \(-72x^{2} + 24x - 1\). B) Expanding \(8(9x - 1/2)^2\) leads to \(576x^{2} - 36x + 2\). C) Expansion of \(8(3x - 1/2)(3x - 1/2)\) gives us \(72x^{2} - 24x + 2\). D) Lastly, \(-8(3x - 1/2)^2\) results in \(-72x^{2} + 24x - 2\).

Identify the correct factorization

By comparing each expanded option with the original expression \(72 x^{2}-24 x+2\), it's clear that option (C) is the only one identical to the original expression. So, the correct factorization of \(72 x^{2}-24 x+2\) is \(8(3x - 1/2)(3x - 1/2)\).