Question

Replace each of the question marks with a value that will make the polynomial a perfect square trinomial.
1. 4x^2+12x+?
2. ?+90x+81
Could someone show me how to solve these?

Take the first:

factor out the 4

4x^2+12x+?
4( x^2 + 3x + ?)

take half the center term, and square it. half is 3/2, squared is 9/4

4( x^2 + 3x + 9/4)
Put the 4 back in...

4x^2 + 12x+9
(2x+3)(2x+3)

Second:
?+90x+81
Notice the last term is a perfect square, its square root is 9. Twice nine is eighteen.
Now to find the missing term, divide 90 by 18: five.

25x^2 + 90x + 81
(5x+9)(5x+9)