Is it possible to factor #y=2x^2 -452x-68#? If so, what are the factors?

1 Answer
Jun 29, 2016

Answer:

#y=2(x-113+sqrt(12803))(x-113-sqrt(12803))#

Explanation:

Step 1: Removing the obvious integer common factor:
#color(white)("XXX")y=2(x^2-226-35)#

From this point on there are no "pretty" factors but...
Step 2: Use the quadratic formula to find the roots

For the general quadratic: #ax^2+bx+c# the roots are given by:
#color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)#

In this case
#color(white)("XXX")x=(226+-sqrt((-226)^2-4(1)(-35)))/(2(1))#

#color(white)("XXXXXX")=(226+-sqrt(51212))/2 = 113+-sqrt(12803)#

So we can continue the factoring as:
#color(white)("XXX")y=2(x-113+sqrt(12803))(x-113-sqrt(12803))#