i need help with operation with polynomial---------------------

Question

1) (x^2 + x - 6) / (x - 2)=

2) 24b^4C^3 / 6b^2c=

3) (3p^2 + pq - 2q^2)/ (p + q)=

Answer 1

1. (X^2 + X - 6) / (X - 2).
Factor the trinomial:
(X + 3)(X - 2) / (X - 2) =
Cancel the (X - 2) factors:
X + 3.

2. 24b^4c^3 / 6b^2c = 4b^2c^2

3. (3p^2 + pq - 2q^2) / (p + 2)
Factor the trinomial using A*C Method:
A * C = 3 * -2 = -6,
3p^2 +3pq-2pq -2q^2
Group the 4 terms into factorable
pairs:
3p^2+3pq -2pq-2q^2,
3p(p + q) -2q(p + q),
Factor out (p + q):
(p + q) (3p - 2q) / (p + q),
CANCEL THE (P + q) factors:
3p - 2q.