Mathematics

Mathematics

Problem

While expressing 4x3−x2+6x2+x+1\dfrac{4x^{3}-x^{2}+6}{x^{2}+x+1} into partial fractions, what must be done immediately after noticing that deg⁡\deg numerator ≥deg⁡\ge\deg denominator? a) Factorise the denominator into linear factors. b) Assume a form Ax+Bx2+x+1\dfrac{Ax+B}{x^{2}+x+1} directly and equate coefficients. c) Perform polynomial long division to write the fraction as a polynomial plus a proper fraction. d) Complete the square in the denominator.

Browse the problem library