Question

what is the greatest common monomial factor of the polynomial below? 15xy³ - 21xy³z a. xy³ b. 2xy³ c. 3xy³

Explanation:

Step1: Find GCF of coefficients

The coefficients are 15 and 21.
Factors of 15: $1, 3, 5, 15$
Factors of 21: $1, 3, 7, 21$
Greatest common factor: $3$

Step2: Find GCF of variable terms

For $x$: Both terms have $x^1$, so GCF is $x$.
For $y$: Both terms have $y^3$, so GCF is $y^3$.
For $z$: Only the second term has $z$, so GCF has no $z$.
Combined variable GCF: $xy^3$

Step3: Multiply GCFs

Multiply coefficient GCF and variable GCF.
$3 \times xy^3 = 3xy^3$

Answer:

C. $3xy^3$