(x - 2) is a factor of :
x3 - x2 + x - 6
x3 + x2 + x + 6
2x3 - 6x2 + 5x - 1
x3 - 4x2 + x - 8
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⇒ x - 2 = 0
⇒ x = 2.
Substituting x = 2 in x3 - x2 + x - 6, we get :
⇒ 23 - 22 + 2 - 6
⇒ 8 - 4 + 2 - 6
⇒ 10 - 10
⇒ 0.
Since, remainder = 0.
∴ x - 2 is a factor of x3 - x2 + x - 6.
Hence, Option 1 is the correct option.
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One factor of x3 - kx2 + 11x - 6 is x - 1. The value of k is :
-6
12
6
-12
Find in each case, the remainder when :
x4 - 3x2 + 2x + 1 is divided by x - 1
x3 + 3x2 - 12x + 4 is divided by x - 2.