How do you factor y=x2−3x−1 ?
1 Answer
Dec 24, 2015
It requires irrational coefficients, but...
Complete the square and use the difference of squares identity to find:
y=x2−3x−1
=(x−32−√132)(x−32+√132)
Explanation:
Note that:
(x−32)2=x2−3x+94
Also, the difference of squares identity can be written:
a2−b2=(a−b)(a+b)
We use this with
y=x2−3x−1
=x2−3x+94−94−1
=(x−32)2−134
=(x−32)2−(√132)2
=((x−32)−√132)((x−32)+√132)
=(x−32−√132)(x−32+√132)
