One of the factors of $1 + x^{3}$ is 1+ x. The other factor is

1 - x + x^{2}

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1 - x - x^{2}

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1 + x + x^{2}

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1 + x - x^{2}

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Solution

The correct option is A $1 - x + x^{2}$
$1 + x^{3} = 1^{3} + x^{3} = (1 + x) (1 - x + x^{2})$

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Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

Q. x + 1 is a factor of the polynomial
(a) x³ + x²– x + 1
(b) x³ + x² + x + 1
(c) x⁴ + x³ + x² + 1
(d) x⁴ + 3x³ + 3x² + x + 1

Q. One of the factors of

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

is:

$x + 1$ is a factor of the polynomial
$A .$ $x^{3} + x^{2} - x + 1$
$B .$ $x^{3} + x^{2} + x + 1$
$C .$ $x^{4} + x^{3} + x^{2} + 1$
$D .$ $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

(x + 1)

is the only factor of

x^{3} + x^{2} + x + 1

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One of the factors of 1+x3 is 1+ x. The other factor is

The correct option is A 1−x+x21+x3=13+x3=(1+x)(1−x+x2)

One of the factors of $1 + x^{3}$ is 1+ x. The other factor is

The correct option is A $1 - x + x^{2}$
$1 + x^{3} = 1^{3} + x^{3} = (1 + x) (1 - x + x^{2})$