The correct options are
.
Further explanation:
In any synthetic division, the dividend polynomial
and the divisor polynomial
can be written as,

Here, the monic polynomial is divided by the polynomial that provides the polynomial after division that is also a factor of the polynomial .
Given:
The synthetic division is given below.
Step by step explanation:
We have to determine the answer among all the options.
Option A:
is a factor of
.
It can be observed from the given synthetic division the polynomial is
that is divisible by the polynomial
.
Therefore, the polynomial
is a factor of the polynomial
.
Therefore, the option A is correct option.
Option B:
is a factor of
.
From the option A, it has been proved that
is a factor of the polynomial

Therefore,
is a not factor of
.
Thus, the option B is not correct option.
Option C: The number
is a root of
.
From the option A, it has been proved that
is a factor of the polynomial
Now substitute 0 for
in the equation
to find the root of the polynomial
as,
It can be seen that the value of
is 4 it means
is not a root of the polynomial
.
Therefore, the option C is not correct option.
Option D: The number
is a root of
.
It can be seen that the value of
is 4 in option C it means
is a root of the polynomial
.
Therefore, the option D is correct option.
Option E:
The option E is also correct as
is the factor of the polynomial
.
Option F:
The option F is not correct as
is not the factor of the polynomial
.
Result:
Therefore, the correct options are
.
Learn more:
- Learn more about the function is graphed below brainly.com/question/9590016
- Learn more about the symmetry for a function brainly.com/question/1286775
- Learn more about midpoint of the segment brainly.com/question/3269852
Answer details:
Grade: Medium school
Subject: Mathematics
Chapter: Synthetic division
Keywords: Synthetic division, polynomial, monic polynomial, function, factor, real number, root, divisible, addition, remainder, quotient, divisor, dividend.