2020 · Q13
What are the values of p and q respectively, if (x-1) and (x+2) divide the polynomial x³+4x²+px+q?
Elementary MathematicsAlgebra
- A1, -6
- B2, -6
- C1, 6
- D2, 6
Explanation
Since x − 1 is a factor, P(1) = 1 + 4 + p + q = 0, i.e. p + q = −5. Since x + 2 is a factor, P(−2) = −8 + 16 − 2p + q = 0, i.e. −2p + q = −8. Subtracting the first equation from the second gives 3p = 3, so p = 1 and then q = −6.