Answer:
Explanation:
To perform synthetic division on this polynomial, we will first write the polynomial in standard form, with the terms arranged in decreasing order of the exponent:
(6x^4 - 12x^3 + 9x - 12)
Then, we will use the following steps to perform synthetic division:
Write the divisor, (x - 2), at the top of the division, and write the constant term of the polynomial, (-12), below it.
Multiply the divisor by the constant term and write the result below the constant term.
Bring down the next term of the polynomial, (9x), and add it to the result from step 2.
Multiply the divisor by the result from step 3 and write the result below it.
Bring down the next term of the polynomial, (-12x^3), and add it to the result from step 4.
Multiply the divisor by the result from step 5 and write the result below it.
Bring down the final term of the polynomial, (6x^4), and add it to the result from step 6.
The final result will be the quotient, and any remainder will be discarded. The result of the synthetic division is shown below:
(x - 2) | -12 9x -12x^3 6x^4
|-------------------
-12 6x -24x^2 36x^3
The quotient is (-12 + 6x - 24x^2 + 36x^3).
Note that we can check our work by multiplying the divisor, (x - 2), by the quotient, (-12 + 6x - 24x^2 + 36x^3), and verifying that the result is equal to the original polynomial.