Factor completely. Remember to look first for a common factor and to check by multiplying. If a polynomial is prime, state this. -81p^2 + 18pq - q^2

Question

Factor completely. Remember to look first for a common factor and to check by multiplying. If a polynomial is prime, state this.   -81p^2 + 18pq - q^2

anonymous · Answer

-81p^2 + 18pq - q^2
= -(9p^2) + 2(9p)(q) - q^2 
You can prove that the polynomial is a perfect square, but for that, it needs to be like this:
81p^2 - 18pq + q^2.
Are you sure that the question is right. If its right, then I think its prime.

anonymous · Answer

yes I am sure, that is the question, I have 2 more questions, This question is worked all the way through but I have no idea what was done to get the answer 

1.  Factor completely. If a polynomial is prime, state this     9t^2 + 14t + 5

t^2 + 7/9t = -5/9 +(7/9)^2
t^2 + 7/9t = (- 45 + 49)/81
(t + 7/9)^2 = 4/81
t + 7/9 = 2/9

t + 7/9 + 2/9  =  t + 9/9  =  t + 1

t + 7/9 - 2/9  = t + 5/9  =  9t + 5

final answer is (t+1)(9t+5)



2. If the area of a rectangle is given by 100g^2 - 220gw + 121w^2 square feet, what are possible expressions for the length and width?