Question

Use synthetic division to solve (x^3 + 1) ÷ (x – 1). What is the quotient?

Answer 1

x^2+x+1+
`(2)/(x-1)`

Explanation:

Answer 2

`(x^(2) +x+1)(x-1)+2`

Explanation:

The synthetic division can be used to divide a polynomial function by a binomial of the form x-c, determining zeros in the polynomial.

step 1: Establish the synthetic division, placing the polynomial coefficients in the first row (if any term does not appear, assign a zero coefficient) and to the extreme left the value of c.

1 | 1 0 0 1

step 2: Lower the main coefficient to the third row.

1 | 1 0 0 1

1

Step 3: Multiply 1 by the main coefficient 1.

1 | 1 0 0 1

1

1

step 4: Add the elements of the second column.

1 | 1 0 0 1

1

1 1

step 5: Then repeat step 4 until the constant term 1 is reached.

1 | 1 0 0 1

1 1 1

1 1 1 2

step 6: Enter the quotient and remainder

quotient:
`x^(2) + x + 1`

remainder: 2

Solution:
`x^(2) + x + 1`
`(x+1)  + 2`