Question

Mr. Johnson asked his students to use synthetic division to divide:

X⁴+ 2x³ - 8x² + 1
given one solution is L = 7.
Below is the work for how 4 different students set up the problem.

Answer 1

To divide the polynomial x⁴ + 2x³ - 8x² + 1 using synthetic division and given that L = 7 as one of the solutions, set up the division as (x - 7) and perform synthetic division to find the quotient.

Step-by-step explanation:

To divide a polynomial using synthetic division, we set up the process as follows:

1. Write the polynomial in descending order, including any missing terms with a coefficient of 0.
2. Identify the divisor and write it in the form (x - L), where L is the given solution.
3. Perform synthetic division by dividing each term of the polynomial by the divisor.
4. Write the quotient as the result of the division, discarding the remainder.

In this case, the polynomial is x⁴ + 2x³ - 8x² + 1, and the given solution is L = 7. To divide the polynomial using synthetic division, we set up the division as follows:

• Divisor: (x - 7)
• Polynomial: x⁴ + 2x³ - 8x² + 1

Performing synthetic division, we find that the quotient is x³ + 9x² + 55x + 384. Therefore, the result of dividing x⁴ + 2x³ - 8x² + 1 by (x - 7) is x³ + 9x² + 55x + 384.