Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm. $x^{3} - 3 x + 1, x^{5} - 4 x^{3} + x^{2} + 3 x + 1$

Yes

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Ambiguous

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Data insufficient

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Solution

The correct option is C No
$x^{3} - 3 x + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ x^{5} - 4 x^{3} + x^{2} + 3 x + 1$ ( $x^{2} - 1$
$x^{5} - - + 3 x^{3} + - x^{2}$
$¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ - x^{3} + 3 x + 1$
$- + x^{3} + - 3 x - + 1 - ------------ -$
$2$
Since remainder is non-zero.
Therfore, $x^{3} - 3 x + 1$ is not a factor of $x^{5} - 4 x^{3} + x^{2} + 3 x + 1$

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g (t) = t^{2} - 3, f (t) = 2 t^{4} + 3 t^{3} - 2 t^{2} - 9 t - 12

g (x) = x^{3} - 3 x + 1, f (x) = x^{5} - 4 x^{3} + x^{2} + 3 x + 1

g (x) = 2 x^{2} - x + 3, f (x) = 6 x^{5} - x^{4} + 4 x^{3} - 5 x^{2} - x - 15

x^{3} - 3 x + 1, x^{5} - 4 x^{3} + x^{2} + 3 x + 1

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

Question 2 (iii)
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

$x^{3} - 3 x + 1, x^{5} - 4 x^{3} + x^{2} + 3 x + 1$

3 x^{4} - 4 x^{3} - 3 x - 1

x - 1

x + 1

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