Use long division to divide. Specify the quotient and the remainder. (x2 + 3x − 1) ÷ (x − 1)

Question

Use long division to divide. Specify the quotient and the remainder.

(x² + 3x − 1) ÷ (x − 1)

I put {x^2+3x-1) over (x-1} but it was marked incorrect

Answer 1

First, note that IF x-1 is the factor then x=1 is the solution;

f(1) = 1^2 +3(1) - 1 = 1 +3 - 1 = 3 so the remainder shall be 3;

As a result, x=1 is not a solution and x-1 is not a factor

x + 4

__________________

x-1 | x^2 + 3x - 1

x^2 - x

______________

4x -1

4x - 4

____________

3

The quotient is x-1 and 3 is the remainder as expected

check step:

(x-1)(x+4) +3 = x^2 +3x - 4 +3 = x^2 +3x - 1