Find in each case, the remainder when :
x3 + 3x2 - 12x + 4 is divided by x - 2.
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x - 2 = 0 ⇒ x = 2.
Required remainder = Value of given polynomial x3 + 3x2 - 12x + 4 at x = 2.
∴ Remainder = (2)3 + 3(2)2 - 12(2) + 4
= 8 + 12 - 24 + 4
= 0.
Hence, remainder = 0.
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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
x4 - 3x2 + 2x + 1 is divided by x - 1
x4 + 1 is divisible by x + 1.
Show that 3x + 2 is a factor of 3x2 - x - 2.