Answer:
(2x + 7) (2x - 9)
Step-by-step explanation:
In order to factor this equation, you can factor it by grouping.
You have to find what numbers multiply to make 4.
4 = 1 x 4 or 2 x 2
In this case, you would want to use 2 x 2.
So, the beginning of the factorization looks like this:
(2x + __) (2x - __)
It must be + and - because both the middle and last part of the equation are negative, but the first part is positive.
From here, you need to figure out what numbers multiply to 63, but also multiplied by 2x = -4x.
Let's try the numbers 7 and 9.
2x(2x) = 4x^2 (squared)
7 (2x) = 14x
-9 (2x) = -18x
14x - 18x = -4x
7 x -9 = -63
If you put all three of these products together, you get 4x^2 - 4x - 63.
So, the factors of this equation are (2x + 7) (2x - 9).
Check by multiplying.
2x (2x) = 4x^2 (squared)
7 (2x) = 14x and -9 (2x) = -18, so 14x - 18x = -4x
7 x -9 = -63
(if you have to find the roots/zeros)
2x + 7 = 0
2x = -7
x = -7/2
2x - 9 = 0
2x = 9
x = 9/2
So the zeros would be: x = -7/2 and 9/2
