SOLUTION: What value is needed to fill in the blank to make this trinomial a perfect square trinomial. 4x2 + __x + 81?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What value is needed to fill in the blank to make this trinomial a perfect square trinomial. 4x2 + __x + 81?      Log On


   

Question 1187975: What value is needed to fill in the blank to make this trinomial a perfect square trinomial. 4x2 + __x + 81?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

recall: a%5E2%2B2ab%2Bb%5E2
in your case a%5E2=4, 2ab=? ,b%5E2=81 =>a=2 and b=9, then 2ab=2%2A2%2A9=36
and your expression is
4x%5E2+%2B+36x+%2B+81
%282+x+%2B+9%29%5E2

Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.

The correct answer is:



        There are  TWO  possible values to place in the blank position:

        One value is  36,  the other value is  -36.

        With  36,  the trinomial is   4x^2 + 36 + 81 = %282x%2B9%29%5E2.

        With  -36,  the trinomial is   4x^2 - 36 + 81 = %282x-9%29%5E2.