Respuesta :
1. a(p–q)+q–p
We take out common factor
To change q - p as p - q we pull out -1
So q - p becomes -1(p - q)
a(p–q)+q–p
a(p–q) -1(p - q)
p -q is in common so we factor out p-q
(p - q) (a - 1)
2. p^2q+r^2–pqr–pr
WE change the order of terms
[tex] p^2q-pqr+r^2-pr [/tex]
We group first two terms and last two terms
[tex] (p^2q-pqr)+(r^2-pr) [/tex]
Now we factor out pq from first group and -r from second group
[tex] pq(p-r) - r(p - r) [/tex]
[tex] (p - r) (pq - r) [/tex]
To write the answer as a product of polynomials we try to factor the polynomial
a(p–q)+q–p
we can write this expression as
a(p-q)+(q-p)
from second parenthesis we can factor out -1 , so we get
a(p-q) -1(p-q)
Now it has two terms a(p-q) and -1(p-q) , from these two terms we can factor out (p-q)
So we get it
(p-q)(a-1)
So we get the polynomial as a product of two polynomials.
Second
[tex] p^2q+r^2- pqr-pr [/tex]
we can rewrite the expression as
[tex] (p^2q- pqr)+(r^2-pr) [/tex]
Now try to factor the groups
factor out "pq" as GCF from first group and "-r" as GCF from second group
[tex] pq(p- r)-r(p-r) [/tex]
Now we can factor it out for final step
[tex] (p- r)(pq-r) [/tex]
