Question

20 factor by gcf
$81a^{2}-24a+27$
$9a(9a^{2}-2a+3)$
$3a(27a^{2}-8a+9)$
$3(27a^{2}-8a+9)$
$3a(27a+8a+9)$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 81, -24, 27.
Factors of 81: 1,3,9,27,81
Factors of 24: 1,2,3,4,6,8,12,24
Factors of 27: 1,3,9,27
Greatest common factor (GCF) = 3

Step2: Factor out GCF from each term

Divide each term by 3:
$81a^2 \div 3 = 27a^2$
$-24a \div 3 = -8a$
$27 \div 3 = 9$
Rewrite the expression: $3(27a^2 -8a +9)$

Step3: Verify no common variable factor

The term 9 has no variable $a$, so no GCF for variables.

Answer:

3(27a²-8a+9)