# How do you factor #7y^2-11y-27#?

##### 2 Answers

#### Explanation:

The difference of squares identity can be written:

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

Use this with

First premultiply by

#28(7y^2-11y-27) = 196y^2-308y-756#

#color(white)(28(7y^2-11y-27)) = (14y)^2-2(14y)(11)+121-877#

#color(white)(28(7y^2-11y-27)) = (14y-11)^2-(sqrt(877))^2#

#color(white)(28(7y^2-11y-27)) = ((14y-11)-sqrt(877))((14y-11)+sqrt(877))#

#color(white)(28(7y^2-11y-27)) = (14y-11-sqrt(877))(14y-11+sqrt(877))#

Hence:

#7y^2-11y-27 = 1/28(14y-11-sqrt(877))(14y-11+sqrt(877))#

(1/28)(14x - 11 - sqrt877)(14x - 11 + sqrt877)

#### Explanation:

There is another classical way.

f(x) = a(x - x1)(x - x2),

where x1 and x2 are the 2 real roots of the quadratic equation

f(x) = 7x^2 - 11x - 27 = 0.

There are 2 real roots:

The factored form will be: