Find in each case, the remainder when :
x4 - 3x2 + 2x + 1 is divided by x - 1
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x - 1 = 0 ⇒ x = 1.
Required remainder = Value of given polynomial x4 - 3x2 + 2x + 1 at x = 1.
∴ Remainder = (1)4 - 3(1)2 + 2(1) + 1
= 1 - 3 + 2 + 1
= 1.
Hence, remainder = 1.
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(x - 2) is a factor of :
x3 - x2 + x - 6
x3 + x2 + x + 6
2x3 - 6x2 + 5x - 1
x3 - 4x2 + x - 8
x3 + 3x2 - 12x + 4 is divided by x - 2.
x4 + 1 is divisible by x + 1.