Question

what is the greatest common monomial factor of the polynomial below? $2xy^{2}+14x^{3}y^{2}z$ \
\
\bigcirc a. $2xy^{2}z$ \
\
\bigcirc b. $2xy^{2}$ \
\
\bigcirc c. $xy^{2}$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 2 and 14. The greatest common factor of 2 and 14 is 2.

Step2: Find GCF of $x$-terms

The $x$-terms are $x^1$ and $x^3$. The GCF is $x^1 = x$.

Step3: Find GCF of $y$-terms

The $y$-terms are $y^2$ and $y^2$. The GCF is $y^2$.

Step4: Find GCF of $z$-terms

The first term has no $z$-term, so the GCF has no $z$.

Step5: Combine all GCFs

Multiply the GCFs from steps 1-4: $2 \times x \times y^2 = 2xy^2$

Answer:

B. $2xy^2$