Final answer:
The possible rational zeros of the polynomial function n(x) = 25x⁷ + 21x³ + 8x + 10 can be found using the Rational Root Theorem. The possible rational zeros are fractions that can be formed from the factors of 10 and the factors of 25.
Step-by-step explanation:
The possible rational zeros of the polynomial function n(x) = 25x⁷ + 21x³ + 8x + 10 can be found using the Rational Root Theorem.
The Rational Root Theorem states that any rational zero of a polynomial function can be expressed as a fraction in the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is 10 and the leading coefficient is 25. The possible rational zeros are the fractions that can be formed from the factors of 10 (±1, ±2, ±5, ±10) divided by the factors of 25 (±1, ±5, ±25).
So, the possible rational zeros are:
- x = ±1/1
- x = ±2/1
- x = ±5/1
- x = ±10/1
- x = ±1/5
- x = ±2/5
- x = ±5/5
- x = ±10/5
- x = ±1/25
- x = ±2/25
- x = ±5/25
- x = ±10/25