Home
Class 12
MATHS
Resolve (x^(3)-6x^(2)+10x-2)/(x^(2)-5x+6...

Resolve `(x^(3)-6x^(2)+10x-2)/(x^(2)-5x+6)` into partial fractions:

Text Solution

AI Generated Solution

To resolve the expression \(\frac{x^3 - 6x^2 + 10x - 2}{x^2 - 5x + 6}\) into partial fractions, we will follow these steps: ### Step 1: Polynomial Long Division Since the degree of the numerator (3) is greater than the degree of the denominator (2), we first perform polynomial long division. 1. Divide \(x^3\) by \(x^2\) to get \(x\). 2. Multiply \(x\) by the entire denominator \(x^2 - 5x + 6\) to get \(x^3 - 5x^2 + 6x\). 3. Subtract this from the original numerator: ...
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise EXERCISE -1 SUBJECTIVE QUESTIONS|1 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SUBJECTIVE QUESTIONS|14 Videos

  • FUNDAMENTAL OF MATHEMATICS

    RESONANCE ENGLISH|Exercise Exercise|135 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise HLP|34 Videos

Similar Questions

Explore conceptually related problems

Resolve (3x^(3)-2x^(2)-1)/(x^(4)+x^(2)+1) into partial fractions.

Resolve (x^(3)+x-1)/((x^(2)+1)(x^(2)+2x+3)) into partial fractions.

3.Resolve (x^(4)-x^(2)+1)/(x^(2)(x^(2)-1)^(2)) into partial fractions.

Resolve (3x^(3)-8x^(2)+10)/((x-1)^(4)) into partial fractions.

Resolve (x^(3)+x^(2)+1)/((x^(2)+2)(x^(2)+3)) into partial fractions.

Resolve (2x^(3)+3x^(2)+5x+7)/((x+1)^(5)) into partial fractions.

Resolve (3x^(2)+x-2)/((x-2)^(2)(1-2x)) into partial fractions.

Resolve (3x^(3)+2x^(2)+x+1)/((x+1)(x+2)) into partial fraction

Resolve (3x^(2)+1)/((x^(2)-3x+2)(2x+1)) into partial fractions.

Resolve (2x^(4)+2x^(2)+x+1)/(x(x^(2)+1)^(2)) into partial fractions.