Answer:

Explanation:

By using the rational root theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -7 & q divides the leading coefficient, 1. Now, let's list out all the possible candidates for p/q by following this theorem.

Now, let's substitute the value of x as these integers. By using the trial & error method, we can see that..

This means that 1 factor of the above equation will be:

So, by using the Factor theorem, we know that, x - k will be the factor of the polynomial for each root k. Now, divide x³ + 6x - 7 by x - 1. We'll the value as:

We now have a quadratic equation with us. By using the biquadratic formula: -b ± √b² - 4ac / 2a, where,
So,

Here, we can see that,

Then, by listing out the solutions that we found, the value of x will be:

