2015 · Q12
The expression x³q²-x³pt+4x²pt-4x²q²+3xq²-3xpt is divisible by
Elementary MathematicsAlgebra
- A(x-1) only
- B(x--3) only
- Cboth (x-1) and (x-3)
- Dneither (x-1) nor (x-3)
Explanation
Grouping by powers of x: (q²−pt)x³ − 4(q²−pt)x² + 3(q²−pt)x = (q²−pt)·x·(x²−4x+3) = (q²−pt)x(x−1)(x−3). Hence it is divisible by both (x−1) and (x−3) (option C).