Answer:To determine whether x - c is a factor of a polynomial using synthetic division, we follow these steps:
1. Write down the coefficients of the polynomial in descending order, including any missing terms with a coefficient of 0. For the given polynomial x³ + 11x² + 24x - 36, the coefficients are 1, 11, 24, -36.
2. Set up the synthetic division table by writing the value of c (in this case, 2) on the left side and the coefficients of the polynomial on the top row.
3. Bring down the first coefficient (1) into the leftmost empty space below the line.
4. Multiply the value in the bottom row (in this case, 2) by the coefficient in the top row (1), and write the result in the next empty space in the bottom row.
5. Add the result from step 4 to the coefficient below it. Write the sum in the next empty space in the bottom row.
6. Repeat steps 4 and 5 until you reach the last coefficient.
The result of the synthetic division should look like this:
2 | 1 11 24 -36
____________________
1 13 50 88
The numbers in the bottom row represent the coefficients of the quotient polynomial obtained by dividing the original polynomial by x - c. In this case, the quotient polynomial is 1x² + 13x + 50 with a remainder of 88.
If the remainder is zero, then x - c is a factor of the polynomial. In this case, the remainder is 88, which is not zero. Therefore, x - 2 is not a factor of the given polynomial x³ + 11x² + 24x - 36.
Step-by-step explanation:
