Question

In the polynomial function F(x)=10x^6+7x−7, according to the rational roots theorem, which is a possible root at point P?

A. -1
B. 1
C. -7
D. 7

Answer 1

According to the Rational Roots Theorem, the possible rational roots of the given polynomial function are -1 and 7.

Step-by-step explanation:

According to the Rational Roots Theorem (also known as the Integer Root Theorem), we can determine the possible rational roots of a polynomial function by finding the divisors of the constant term (in this case, -7) and the leading coefficient (in this case, 10), and then testing each possible root using synthetic division or long division.

The possible rational roots of the polynomial function F(x) = 10x^6 + 7x - 7 are the divisors of 7 divided by the divisors of 10. So, we need to consider the divisors of 7 (-7, -1, 1, 7) divided by the divisors of 10 (-10, -5, -2, -1, 1, 2, 5, 10). From the given options, A (-1) and D (7) are two possible rational roots of the polynomial function F(x).