Question

if X + 1 and x minus 1 are the factor of m x cube + x square - 2 X + n find the value of M and n.

Answer 1

OK

==> X+1 = 0      ;   X-1 = 0

==> X = -1 ; 1

POLYNOMIAL = MX³+X²-2X+N

P[1] = M[1]³+[1]²-2[1]+ N

P[1] = M + 1 - 2 + N

==> M+N - 1

==> M+N = 1 ....{1}

P[-1] = M[-1]³+[-1]²-2[-1]+N

==> -M+1+2+N ==> -M+N+3

==> -M+N = -3...........[2]

EQ[1] AND [2]

M+N = 1

-M+N = -3

2N = -2

==> N = -1

PUTTING VALUE IN EQ[2]

-M+N = -3

-M-1 = -3

-M = -2

M = 2

I HOPE ITS HELPFUL FOR YOU