Hello, victorfk06!
Are you familiar with the Factor Theorem?Factor the polynomial: .
Given a polynomial , if , then is a factor of
And the Rational Roots Theorem?
A rational root of a polynomial equation is of the form: .
. . where is a factor of the constant term,
. . and is a factor of the leading coefficient.
We want a number which makes the polynomial equal zero.
There are eight candidates.
. . The numerator is a factor of 1: .
. . The denominator is a factor of 6: .
The possible rational roots are: .
And we find that works: .
Hence, is a factor.
Using long division, we find that:
. . . . . as emathinstruction already pointed out.
We find that the quadratic expression doesn't factor . . . so we're done!