Posted by **Christian** on Monday, May 21, 2007 at 10:41pm.

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)

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