-a%5E(4)-5a%5E(2)%2B36.jpeg "(xi) A^(4)-5a^(2)+36")
Factoring the Expression: a⁴ - 5a² + 36
This expression, a⁴ - 5a² + 36, can be factored using a technique similar to factoring quadratic equations. Here's how:
1. Substitute a Variable:
- Let's substitute x = a². This allows us to rewrite the expression as: x² - 5x + 36
2. Factor the Quadratic Expression:
- Now, we have a standard quadratic expression that we can factor. However, this specific quadratic doesn't factor nicely into integers. You can check this using the quadratic formula or by trying to find factors of 36 that add up to -5.
3. Leave the Expression in Factored Form:
- Since we can't factor the quadratic expression further, we can leave the expression in its factored form using the substitution we made earlier: (a²)² - 5(a²) + 36
Final Result:
The factored form of the expression a⁴ - 5a² + 36 is (a²)² - 5(a²) + 36.
Important Note:
Although we can't factor the expression further using integers, there are other methods to express it in a different form, such as using complex numbers. However, the most straightforward way to factor this expression is the one described above.