How do you factor -p^{2}+4p-4=0?

1 Answer
Mar 23, 2018

-(p-2)^2=0
This involves factoring out the negative from the trinomial.

Explanation:

You want the leading coefficient on the p^2 to be positive. This means that you should factor out the negative, which will switch the signs.

=> -(p^2-4p+4)=0

Now that the negative is factored out, you should factor the rest like normal. As p^2 has no coefficient, the p in the factorization must have no coefficient. Seeing the 4's, 2 should pop into your head, because both 2+2 and 2*2 equal 4. The constant is positive, which implies a -2, because -2^2=4.

These conclusions lead to:

=> (p-2)^2=0

Now add the negative in front, for:

=> -(p-2)^2=0

You can test the answer by using FOIL:

=> -((p-2)(p-2))=0
=> -(p^2-4p+4)=0

Distribute the negative:

=> -p^2+4p-4=0