Question

Use synthetic division to solve (x^4 – 1) ÷ (x – 1). What is the quotient?

Answer 1

Quotient is:

${ x }^{ 3 }+{ x }^{ 2 }+x+1$

Remainder: 0

Answer and workings in the attachment below.

Answer 2

Answer:  $x^3+x^2+x+1$

Step-by-step explanation:

Here, the dividend is $x^4+0x^3+0x^2+0x-1$

While divisor is  x - 1

In the synthetic division,

We will follow the following steps,

Step 1) Write the coefficient of the dividend in the decreasing order of degree,

Hence, the element in the first row under the division sign are 1, 0, 0, 0, - 1

Step 2) By putting x - 1= 0, we get x = 1

Hence, write down 1 outside the sign,

Here the problem is set up correctly, So, bring the leading coefficient (first number) straight down.

Step 3)  Multiply the number in the division box with the number that we brought down and put the result in the next column. Then, Add the two numbers together and write the result in the bottom of the row.

Step 4) Repeat the third step until you get the last element ( here the last element is 0,

Thus, We get numbers in the third row, 1, 1, 1, 1 ( Except 0 )

⇒ Quotient is  $x^3 + x^2 + x + 1$