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What number has to fill in the blank to make this a perfect square trinomial
9x2 + ___x + 144
Write this square trinomial in factored form
to find the middle term, we want to use the generic quadratic equation
a2 + 2ab + b2
9x2 + ____ + 144
to find the value of a and b, let's take the square root of each
2ab =
2(3x)(12) = 72x
The middle term is 72 x
to factor this trinomial, we want to recognize that each coefficient is divisible by 9
so let's factor out that 9
9x2 + 72x + 144
9(x2 + 8x + 16)
looks like we have a perfect square
what can be multiplied to get 16 and ± to get 8
the answer is, of course, 4
9(x2 + 4x + 4x + 16)
factored form = 9(x + 4)2