Question

find the greatest common factor of the expressions
$33cx^5$
$9c^4x^6$
$21c^4x^2$
show your work here
hint: to add an exponent ($x^8$), type \exponent\ or press \^\
enter your answer

4.
find the greatest common factor of the expressions
$-15a^5w^3$
$10a^3w^2$
$55a^2w^2$
show your work here
hint: to add an exponent ($x^8$), type \exponent\ or press \^\

Explanation:

Problem 1:

Step1: Factor coefficients

Prime factors:
$33 = 3 \times 11$, $9 = 3^2$, $21 = 3 \times 7$
GCF of coefficients: $3$

Step2: Find GCF of $c$-terms

Exponents of $c$: $1, 4, 4$
GCF exponent: $1$, so $c^1 = c$

Step3: Find GCF of $x$-terms

Exponents of $x$: $5, 6, 2$
GCF exponent: $2$, so $x^2$

Step4: Multiply GCF parts

$3 \times c \times x^2 = 3cx^2$

Problem 2:

Step1: Factor coefficients

Prime factors:
$15 = 3 \times 5$, $10 = 2 \times 5$, $55 = 5 \times 11$
GCF of coefficients: $5$

Step2: Find GCF of $a$-terms

Exponents of $a$: $5, 3, 2$
GCF exponent: $2$, so $a^2$

Step3: Find GCF of $w$-terms

Exponents of $w$: $3, 2, 2$
GCF exponent: $2$, so $w^2$

Step4: Multiply GCF parts

$5 \times a^2 \times w^2 = 5a^2w^2$

Answer:

1. $3cx^2$
2. $5a^2w^2$