While expressing into partial fractions

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

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.

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