Theory question 104
PolynomialsIf (3x2 + 3x − 2)/((x − 1)(x + 1)) ≡ P + Q/(x − 1) + R/(x + 1), find the values of Q and R.
Show the model answer
Model answer
3x² + 3x − 2 = 3(x² − 1) + 3x + 1, so P = 3 and (3x + 1)/((x − 1)(x + 1)) = Q/(x − 1) + R/(x + 1).
3x + 1 = Q(x + 1) + R(x − 1). x = 1: 4 = 2Q, Q = 2. x = −1: −2 = −2R, R = 1.
Explanation
Divide first, because the top and bottom have the same degree.