Question

5. How many possible rational roots are there for the polynomial P(x) = 10x³ + 6x² + 4x +4?

a.8
b.10
c.16
d.4

Answer 1

By the Rational Root Theorem, the possible rational roots of a polynomial are of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term of P(x) is 4, whose factors are ±1 and ±4. The leading coefficient is 10, whose factors are ±1, ±2, ±5, and ±10.

So, the possible rational roots of P(x) are: ±1/1, ±2/1, ±4/1, ±1/10, ±2/10, ±5/10, and ±10/10. This gives us a total of 8 possible rational roots.

Therefore, the answer is a. 8.

Explanation: