Question

completely factor the polynomial, if possible.

\\18x^2 - 2\\

Explanation:

Identify the greatest common factor

Using the Factoring Polynomials by GCF knowledge point

$$ \text{GCF}(18x^2, 2) = 2 $$

$$ 18x^2 - 2 = 2(9x^2 - 1) $$

Factor the remaining binomial

Using the Difference of Squares knowledge point

$$ 9x^2 - 1 = (3x)^2 - (1)^2 $$

$$ (3x)^2 - (1)^2 = (3x - 1)(3x + 1) $$

Write the completely factored form

Using the Factoring Polynomials knowledge point

$$ 18x^2 - 2 = 2(3x - 1)(3x + 1) $$

Answer:

\(2(3x - 1)(3x + 1)\)