WAEC Further Mathematics 2025 Theory question 104

Theory question 104

Polynomials

Resolve (2x − 7)/(25x − 24 − 6x²) into partial fractions.

Show the model answer

Model answer

25x − 24 − 6x² = −(6x² − 25x + 24) = −(2x − 3)(3x − 8) = (2x − 3)(8 − 3x).
(2x − 7)/((2x − 3)(8 − 3x)) = A/(2x − 3) + B/(8 − 3x); 2x − 7 = A(8 − 3x) + B(2x − 3).
x = 3/2: −4 = A(7/2), A = −8/7. x = 8/3: −5/3 = B(7/3), B = −5/7.
Answer: −8/(7(2x − 3)) − 5/(7(8 − 3x)).

Explanation

Factorise the denominator first, then substitute the roots.