How do you divide (2x^2-3x+2)/(x - 1)?

2 Answers
Aug 10, 2017

2x-1 and remainder of (-3)/(x-1)

Explanation:

color(white)(.............)ul(2x-1)
color(white)(aa)x-1|2x^2-3x-2
color(white)(..............)ul(2x^2-2x)
color(white)(........................)-x-2
color(white)(.........................)ul(-x+1)
color(white)(..............................)-3

color(magenta)((2x^2-3x-2) / (x-1) = 2x-1 and remaindercolor(magenta)((-3)/(x-1)

Aug 10, 2017

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

or

(2x^2-3x-2)/(x-1) = 2x-1 - 3/(x-1)

Explanation:

In each section of the 'long division', the values on the quotient depend on what factor of the highest degree of the divisor can fit into the highest degree of the dividend. For example, x fits 2x times into 2x^2, x fits -1 times into -x

{: (,,,2x,-1), (,,"---","---","---"), (x-1,")",2x^2, -3x, -2), (,,2x^2,-2x,), (,,"---","---",), (,,,-x,-2), (,,,-x,+1), (,,"---","---","---"), (,,,,-3) :}

Therfore,

(2x^2-3x-2)/(x-1) = 2x-1 - 3/(x-1)

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