How do you factor x² + 9?
How do you factor x² + 9?
Aniket Singh , 8 Months ago
Grade
10 grade maths> How do you factor x² + 9?...
1 AnswersAskiitians Tutor Team
Factoring the expression x² + 9 involves recognizing that it cannot be factored into real numbers since it does not fit the standard forms of factoring.
Understanding the Expression
The expression x² + 9 is a sum of squares. In algebra, sums of squares do not factor neatly over the real numbers. However, it can be expressed using complex numbers.
Using Complex Numbers
To factor x² + 9 using complex numbers, we can rewrite it as:
- x² + 9 = x² + (3i)²
Here, i is the imaginary unit, defined as the square root of -1. Thus, we can factor it as:
- (x + 3i)(x - 3i)
Summary
In summary, while x² + 9 cannot be factored over the real numbers, it can be expressed as (x + 3i)(x - 3i) in the realm of complex numbers.
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