Question

factor out the gcf
18x³ + 81x - 27
3 (6x³ + 27x - 9)
9 (2x² + 9x - 3)
9 (2x³ + 9x - 3)
9x (2x² + 9x - 3)

Explanation:

Step1: Find GCF of coefficients

The coefficients are 18, 81, -27. Prime factors:
18 = 2×3², 81 = 3⁴, 27 = 3³. GCF of 18, 81, 27 is 9.

Step2: Find GCF of variables

Terms: \(18x^3\), \(81x\), \(-27\). The variable part: \(x^3\), \(x\), (no variable). GCF of variables is 1 (since -27 has no \(x\)).

Step3: Factor out GCF (9)

Divide each term by 9:
\(18x^3 ÷ 9 = 2x^3\), \(81x ÷ 9 = 9x\), \(-27 ÷ 9 = -3\).
So, \(18x^3 + 81x - 27 = 9(2x^3 + 9x - 3)\).

Answer:

9 (2x³ + 9x - 3) (the third option)