2021 · Q2
Which one of the following is a factor of the polynomial (x − 1)(x − 2)(x − 4) − 90 ?
Elementary MathematicsAlgebra
- Ax + 14
- Bx − 14
- Cx − 6
- Dx − 7
Explanation
By the factor theorem, (x − 7) is a factor exactly when x = 7 is a root. Substituting x = 7 gives (7−1)(7−2)(7−4) − 90 = 6 × 5 × 3 − 90 = 90 − 90 = 0. Hence (x − 7) divides the polynomial. The other listed binomials do not vanish the expression, so the answer is option (d).