Solve Question number 65 -
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let P(x)= 2x^m+x³-3x²-26
if p(x) is divided by (x-2),
remainder = 226
p(2) =226 [by remainder theorem
2*2^m+2³-3*2²-26 =226
2*2^m +8-12-26 =226
2*2^m +8-38 =226
2*2^m-30 =226
2*2^m =226+30
2*2^m =256
2^m =256/2
2^m =128[since 128 = 2*2*2*2*2*2*2]
2^m =2^7
m=7 [since if a^m = a^n then m=n]
ans is m=7
if p(x) is divided by (x-2),
remainder = 226
p(2) =226 [by remainder theorem
2*2^m+2³-3*2²-26 =226
2*2^m +8-12-26 =226
2*2^m +8-38 =226
2*2^m-30 =226
2*2^m =226+30
2*2^m =256
2^m =256/2
2^m =128[since 128 = 2*2*2*2*2*2*2]
2^m =2^7
m=7 [since if a^m = a^n then m=n]
ans is m=7
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