How do you factor #6x^2-21#?

1 Answer
Sep 2, 2016

Answer:

#6x^2-21 = 3(sqrt(2)x-sqrt(7))(sqrt(2)x+sqrt(7))#

Explanation:

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We use this with #a=sqrt(2)x# and #b=sqrt(7)# as follows:

#6x^2-21 = 3(2x^2-7)#

#color(white)(6x^2-21) = 3((sqrt(2)x)^2-(sqrt(7))^2)#

#color(white)(6x^2-21) = 3(sqrt(2)x-sqrt(7))(sqrt(2)x+sqrt(7))#