Math Questions and Answers

Start Your Free Trial

`(2x^3 - 4x^2 - 15x + 5)/(x^2 - 2x - 8)` Write the partial fraction decomposition of the rational expression.

Expert Answers info

gsarora17 eNotes educator | Certified Educator

calendarEducator since 2015

write762 answers

starTop subjects are Math, Science, and Business

`(2x^3-4x^2-15x+5)/(x^2-2x-8)`

Since the above rational expression is an improper rational expression , so the first step is to divide and express the expression as a sum of simpler fractions such that the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator.

Dividing the polynomial using long division method yields,

`(2x^3-4x^2-15x+5)/(x^2-2x-8)=2x+(x+5)/(x^2-2x-8)`  

Since the polynomials do not completely divide, we have to continue with the partial fractions of the remainder expression,

Now let's factorize the denominator of the remainder expression,

`x^2-2x-8=x^2-4x+2x-8`

`=x(x-4)+2(x-4)`

`=(x+2)(x-4)`

(The entire section contains 2 answers and 385 words.)

Unlock This Answer Now


check Approved by eNotes Editorial

Luca B. eNotes educator | Certified Educator

calendarEducator since 2011

write5,348 answers

starTop subjects are Math, Science, and Business