The binomial that is a factor of the polynomial is (x-2).
STEP - BY - STEP EXPLANATION
What to find?
The binomial that is a factor of the polynomial.
Given:
P(x) =3x³ - 11x² -2x + 24
The factor can be determine by simply finding the zeros of the polynomial.
The zeros of a polynomial when substituted into the polynomial makes it zero.
From the given option, we shall test to see which makes the polynomial zero.
Substitute x=2 into the given polynomial and simplify.
That is;
p(3) = 3(2)³ - 11(2)² -2(2)+ 24
=3(8) - 11(4) - 2(2) + 24
=24 - 44 - 4 + 24
=0
Hence, p(x) = 0 when x=2.
This implies x-2 is a factor of the polynomial.
Since x=2 is the only digit among the option that makes p(x) =0, then (x-2) is the only binomial that is a factor among the options given.