Question

Factor:

12x2 - 21

A) (6x + 3)(2x + 7)
B) (12x + 7)(x + 3)
C) (3x + 7)(4x - 3)
D ) prime

Answer 1

When you factor this, the easiest way to do it is to set the expression equal to 0 and then factor out anything common to get it into a simpler form. 3 goes into both 12 and 21.
`3(4x^2-7)=0`. Now of course,
`3\\eq 0`, so that means that
`4x^2-7=0`. We solve for x to get
`4x^2=7` and
`x^2=(7)/(4)` and finally that
`x=\sqrt{(7)/(4)}`. 4 is a perfect square that can be simplified, so that leaves us with
`x=+/-(√(7))/(2)`. If we expand that back out we have the 2 factors as
`(4x-√(7))(4x+√(7))`. Obviously, that is not one of your choices, so your choice is the last one: prime.