Answer:
The HCF of these polynomials is (p+2q).
Step-by-step explanation:
First of all, we need to factorize each polynomial:
a) [tex]p^{2}+4pq+4q^{2}[/tex]
[tex]=p^{2}+4pq+(2q)^{2}[/tex]
[tex]=(p+2q)^{2}[/tex]
b) [tex]p^{4}+8pq^{3}[/tex]
[tex]=p(p^{3}+8q^{3})[/tex]
[tex]=p(p^{3}+(2q)^{3})[/tex]
[tex]=p(p+2q)(p^{2}-2pq+(2q)^{2})[/tex]
c) [tex]3p^{4}-10p^{2}q^{2}+p^{3}q[/tex]
[tex]=p^{2}(3p^{2}-10q^{2}+pq)[/tex]
[tex]=p^{2}(3p-5q)(p+2q)[/tex]
Therefore, the HCF of these polynomials is (p+2q).
I hope it helps you!
