How do you factor x2+25 completely?
2 Answers
This can only be factored using non-Real Complex coefficients:
x2+25=(x−5i)(x+5i)
Explanation:
Notice that if
The difference of squares identity can be written:
a2−b2=(a−b)(a+b)
We can write
x2+25=x2−(5i)2=(x−5i)(x+5i)
where
Explanation:
There are two methods.
1. By using the general expression to find the roots of a quadratic expressions. If
Then
In the given expression
As such the quadratic has only imaginary roots. These can be calculated and factors found as
- By inspection. For the given problem
x2+25 can be written as
x2−(5ι)2 whereι≡√−1
To find the two factors usex2−y2=(x+y)(x−y)
Hence,x2−(5ι)2=(x+5ι)(x−5ι)