Question
Question: When the polynomial 5x<sup>3</sup> + Mx + N is divided by x<sup>2</sup> + x + 1 the remainder is 0. ...
When the polynomial 5x3 + Mx + N is divided by x2 + x + 1 the remainder is 0. The value (M + N) is equal to –
A
–3
B
4
C
–5
D
15
Answer
–5
Explanation
Solution
Let f(x) = 5x3 + Mx + N
Also x2 + x + 1 = (x –ω) (x – ω2)
f(ω) = 5 + Mω + N = 0
f(ω2) = 5 + Mω2 + N = 0
⇒ M = 0; N = –5
⇒ M + N = –5