Question

Write the expression as a product of polynomials:

a(p–q)+q–p

p^2q+r^2–pqr–pr

PLZ ANSWER ASAP

Answer 1

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

`p^2q-pqr+r^2-pr`

We group first two terms and last two terms

`(p^2q-pqr)+(r^2-pr)`

Now we factor out pq from first group and -r from second group

`pq(p-r) - r(p - r)`

`(p - r) (pq - r)`

Answer 2

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

`p^2q+r^2- pqr-pr`

we can rewrite the expression as

`(p^2q- pqr)+(r^2-pr)`

Now try to factor the groups

factor out "pq" as GCF from first group and "-r" as GCF from second group

`pq(p- r)-r(p-r)`

Now we can factor it out for final step

`(p- r)(pq-r)`