Question

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

Answer 1

Answer:

$(x^{2} +x+1)(x-1)+2$

Step-by-step 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:   $x^{2} + x + 1$ $(x+1)  + 2$

Answer 2

Answer:

x^2+x+1+$\frac{2}{x-1}$

Step-by-step explanation: