Question

Divide Using Synthetic Division (x^3-14x+8)/(x+4)

Answer 1

Synthetic division is a method used to divide polynomials. By following a series of steps, you can find that the given polynomial x^3 - 14x + 8 divided by x + 4 yields a quotient of x^2 - 4x + 2 with no remainder.

Step-by-step explanation:

To divide the polynomial x^3 - 14x + 8 by x + 4 using synthetic division, you follow these steps:

1. Write down the coefficients of the polynomial: 1, 0, -14, 8. (Notice the zero represents the missing x^2 term.)
2. Write the zero of the divisor x + 4 which is -4.
3. Bring down the leading coefficient (1) to the bottom row.
4. Multiply the number on the bottom row by -4 and write the result under the next coefficient.
5. Add the numbers in the second column and write the result in the bottom row.
6. Repeat steps 4 and 5 for the remaining columns.
7. The bottom row, except the last number, gives the coefficients of the quotient polynomial, and the last number is the remainder.

After performing these steps, you'll find that the quotient is x^2 - 4x + 2 and the remainder is 0, which means x + 4 is a factor of the given polynomial.