Question

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

x3 -x2+x-1
O x3
x+x2+x+1
x3-2

Answer 1

C

Explanation:

Answer 2

The quotient is x³+x²+x+1

Explanation:

=(x^4-1) ÷ (x-1)

=(x^4-1)/ (x-1)

Solve the numerator by using perfect square formula:

⇒x^4-1 = (x²-1)(x²+1)

=(x²-1)(x²+1)/(x-1)

Further solve the numerator by using perfect square formula:

=(x+1)(x-1)(x²+1)/(x-1)

Cancel the like terms of numerator and denominator

We get;

=(x+1)(x²+1)

Multiply the terms:

=x³+x+x²+1

Re-arrange the terms:

=x³+x²+x+1

Hence the quotient is x³+x²+x+1....