Question

Find the HCF: Image attached

Answer 1

The HCF of these polynomials is (p+2q).

Explanation:

First of all, we need to factorize each polynomial:

a)
`p^(2)+4pq+4q^(2)`

`=p^(2)+4pq+(2q)^(2)`

`=(p+2q)^(2)`

b)
`p^(4)+8pq^(3)`

`=p(p^(3)+8q^(3))`

`=p(p^(3)+(2q)^(3))`

`=p(p+2q)(p^(2)-2pq+(2q)^(2))`

c)
`3p^(4)-10p^(2)q^(2)+p^(3)q`

`=p^(2)(3p^(2)-10q^(2)+pq)`

`=p^(2)(3p-5q)(p+2q)`

Therefore, the HCF of these polynomials is (p+2q).

I hope it helps you!