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: