Answer :
The polynomial function f(x) = x⁴ + 21x² − 100 can be factored as (x² + 25)(x + 2)(x − 2).
The goal is to factor the polynomial function f(x) = [tex]x^{4} +21x^{2} -100[/tex]. To do this, we look for a substitution method to simplify the problem.
- Let's use y = [tex]x^{2}[/tex], hence the equation becomes:
[tex]y^{2} +21y-100[/tex]
2. Now, we factor the quadratic in terms of y. We need to find two numbers that multiply to -100 and add up to 21. These numbers are 25 and -4. Thus, the quadratic factors as:
(y + 25)(y − 4)
3. Replacing y back with[tex]x^{2}[/tex], we get:
([tex]x^{2}[/tex] + 25)([tex]x^{2}[/tex] − 4)
4. Finally, we can factor further:
([tex]x^{2}[/tex] + 25)(x + 2)(x − 2)
Thus, the factored form of f(x), [tex]x^{4} +21x^{2} -100[/tex] = 0 is ([tex]x^{2}[/tex] + 25)(x + 2)(x − 2).
x^4 + 21x^2 − 100
= (x^2 - 4)(x^2 + 25)
= (x + 2)(x - 2)(x^2 + 25)
hope it helps
= (x^2 - 4)(x^2 + 25)
= (x + 2)(x - 2)(x^2 + 25)
hope it helps
