Question

Which expression represents the correct form for the quotient and remainder, written as partial fractions, of 6x^3 + 15x^2 +20x +36

Answer 1

To express the given expression as partial fractions, factor the polynomial and write it as a sum of simpler fractions with unknown constants.

Step-by-step explanation:

The expression 6x^3 + 15x^2 + 20x + 36 can be written as the sum of partial fractions by factoring the polynomial. To do this, we need to factor the polynomial and represent it as a sum of simpler fractions. We have:

6x^3 + 15x^2 + 20x + 36 = (2x^2 + 3x + 6) * (3x + 6) = (2x + 3) * (x + 2) * (3x + 6)

Therefore, the expression can be rewritten as:

6x^3 + 15x^2 + 20x + 36 = A/2x + 3 + B/x + 2 + C/3x + 6

where A, B, and C are constants.