the correct answer option is (2x-3)(2x+3).
step-by-step explanation:
we are given the following expression and we are to factorize it:
![4x^2-0x-9](/tex.php?f=4x^2-0x-9)
we are to find such factors that when multiplied they give a result of 36 (9 x 4 = 36) and when added they give a result of 0.
the two such factors of 36 are negative six and postive six.
factorizing the given expression to get:
![4x^2-0x-9](/tex.php?f=4x^2-0x-9)
![=4x^2-6x+6x-9\\\\=2x(2x-3)+3(2x-3)\\\\=(2x+3)(2x-3)\\\\=(2x-3)(2x+3)](/tex.php?f==4x^2-6x+6x-9\\\\=2x(2x-3)+3(2x-3)\\\\=(2x+3)(2x-3)\\\\=(2x-3)(2x+3))
therefore, the correct factorization of
is (2x-3)(2x+3).