Question

Which of the following is a factor of (x⁴-27x²-14x+120)

A. x+2
B. x-3
C. x+4
D. x+5

Answer 1

To determine which of the given options is a factor of the polynomial (x⁴-27x²-14x+120), use synthetic division.

Step-by-step explanation:

To determine which of the given options is a factor of the polynomial (x⁴-27x²-14x+120), we can use synthetic division.

We will use option C, x+4, as an example:

1. Arrange the terms of the polynomial in descending order: x⁴-27x²-14x+120
2. Write the coefficient of each term below the horizontal line: 1 -27 -14 120
3. Place the divisor (x+4) outside the synthetic division bracket and divide the first coefficient by it: 1 ÷ -4 = -0.25
4. Multiply the divisor by the quotient obtained: -4 x -0.25 = 1
5. Add the result to the second coefficient: -27 + 1 = -26
6. Repeat steps 3-5 until all coefficients have been evaluated:
   • -26 x -4 = 104, -14 + 104 = 90
   • 90 x -4 = -360, 120 + -360 = -240

The result of the synthetic division shows that there is a remainder of -240, indicating that x+4 is not a factor of the polynomial. Therefore, option C is not a factor of the given polynomial. You can also apply this method to check the other options and identify the correct factor.