Question

factor out the greatest common factor.
36x² + 18x + 54
?(2x² + x + 3)

Explanation:

Step1: Find GCF of coefficients

The coefficients are 36, 18, 54. Prime factors:
36 = 2×2×3×3, 18 = 2×3×3, 54 = 2×3×3×3.
GCF is 2×3×3 = 18.

Step2: Divide each term by GCF

Divide \(36x^2\) by 18: \(\frac{36x^2}{18} = 2x^2\)
Divide \(18x\) by 18: \(\frac{18x}{18} = x\)
Divide 54 by 18: \(\frac{54}{18} = 3\)

So, \(36x^2 + 18x + 54 = 18(2x^2 + x + 3)\).

Answer:

18