Question

Find the remainder when x^3 - 3x^2 - 3x -1 is divided by x-1
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Answer 1

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Find the remainder when x³ - 3x² - 3x - 1 is divided by x - 1

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We can use remainder theorem to find the remainder of the polynomial.

Remainder theorem is nothing but applying the value of x to the polynomial.

x - 1 = 0

x = 1

Now we apply the value of x to the polynomial.

Let,

p(x) = x³ - 3x² - 3x - 1

p(1) = (1)³ - 3(1)² - 3(1) -1

= 1 - 3 - 3 - 1

= - 3 - 3

= - 6

∴ The remainder of the polynomial x³ - 3x² - 3x - 1 is - 6