Question
If polynomial P(x) = x3 - 3x2 +
5x-3 is divided by polynomial G (x) = x2 - 2, the quotient and remainder are:Solution
Dividend = Divisor × quotient + remainder x3 - 3x2 + 5x - 3 = (x2 - 2) × (x - 3) + (7x - 9) x3 - 3x2 + 5x - 3 = (x3 - 3x2 - 2x + 6) + (7x - 9) x3 - 3x2 + 5x - 3 = x3 - 3x2 + 5x - 3 LHS = RHS Hence by using the long division method, the quotient and remainder of the polynomial p(x) = x3 - 3x2 + 5x - 3 when divided by the polynomial g(x) = x2 - 2 are x - 3 and 7x - 9 respectively.
What will come in place of (?) question mark in the given number series.
16, 24, 51, 115, 240, ?
Find the missing number in the given number series.
512, 128, 32, 8, ?, 171, 79, 88, 152, ?, 393
15, 31, 67, 131, ?, 375
1, 26, 75, 156, 277, ?
7 29 61 ? 211 349
...18   29   16   31   ?   33
72, 82, 62, 102, 22, ?
?, 15, 45, 225, 1575, 14175
166    156    136   ?     66    16
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