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Relation between Roots and Coefficients for Quadratic

Factors of ...

Question

Factors of $p (x) = x^{3} - x^{2} - x + 1$ are

x + 1

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x - 1

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x^{2} + 1

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x - 2

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Solution

The correct options are
C $x - 1$
D $x + 1$
$p (x) = x^{3} - x^{2} - x + 1$
$= x^{2} (x - 1) - (x - 1)$
$= (x - 1) (x^{2} - 1)$ or
$= (x - 1) (x + 1) (x - 1)$ are the factors of the given polynomial.

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Similar questions

g (x)

p (x)

p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1

p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2

p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3

x - 1, x - 3

x + 1

P (x)

3

P (x)

x^{2} + 1

x^{2} - 1

x^{2} - 4 x + 3

\frac{x^{3} + x^{2} + x + 1}{x^{3} - x^{2} + x - 1} = \frac{x^{2} + x + 1}{x^{2} - x + 1}

x

(i) p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1

(i i) p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2

(i i i) p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3

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