Question

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

Answer 1

The correct answer is:

x³+x²+x+1.

Explanation:

First we write the polynomial out with all of the other powers of x, using 0 as their coefficients:

(1x⁴+0x³+0x²+0x-1)÷(x-1)

To perform synthetic division, we write the coefficients of the dividend in a row:

1 0 0 0 1

We take the 1 from x-1 and use it in the box. We then drop the first 1 from the row of coefficients down.

We multiply our 1 in the box by the 1 at the bottom; this is 1 and goes under the first 0 to the right of the 1 in the coefficients row. We now add this 0+1; this is 1 and goes at the bottom beside the other 1.

Multiply this by 1; this is 1 and goes under the second 0 from the left in the row of coefficients. Add this to the 0; this is 1 and goes at the bottom, to the right of the other two 1's.

Multiply this by 1; this is 1 and goes under the third and last 0 in the row of coefficients. Add this to the 0; this is 1 and goes at the bottom, to the right of the other three 1's.

Multiply this by 1; this is 1 and goes under the -1 in the row of coefficients. Add this to the -1; this is 0 and goes at the bottom, to the right of the four 1's. This 0 means there is no remainder and the quotient was evenly divided. It gives us

1 1 1 1 0

This means we have 1x³+1x²+1x+1 with no remainder.

Answer 2

Answer:

The quotient is $1x^3+1x^2+1x+1$

Step-by-step explanation:

Given the expression $(x^4-1)$. we have to divide this expression by (x-10 by using synthetic division.

Steps in synthetic division

Step 1: Write the coefficients of x in descending order in the dividend inside the division table.

Step 2: Drop down the first coefficient of the dividend below the division symbol.

Step 3: Multiply the drop-down by the divisor, and write the answer diagonally in the next columns.

Step 4: Add down the column.

Step 5:  Repeat Steps 4 and 5 until the last column.

Now, as shown in synthetic division table, the quotient is

$1x^3+1x^2+1x+1$ and remainder is 0