$3 x^{3} - 5 x^{2} + 2 x + 1, 3 x - 2 x^{2} - x^{3}, 2 x^{2} - 7 x + 9$

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Solution

Given expressions: $3 x^{3} - 5 x^{2} + 2 x + 1, 3 x - 2 x^{2} - x^{3}, 2 x^{2} - 7 x + 9$
Finding the sum of expressions:
$3 x^{3} - 5 x^{2} + 2 x + 1$
$- x^{3} - 2 x^{2} + 3 x$
$2 x^{2} - 7 x + 9$
$2 x^{3} - 5 x^{2} - 2 x + 10$
Hence, sum of the given expression will be $2 x^{3} - 5 x^{2} - 2 x + 10$

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Similar questions

$3 x^{3} + 2 x^{2} + 3 x + 2$ =?

(a) $(3 x - 2) (x^{2} - 1)$

(b) $(3 x - 2) (x^{2} + 1)$

(d) $(3 x + 2) (x^{2} + 1)$

Using the FActor theroem, show that:
(i) (x-2) is a factor fo $x^{3} - 2 x^{2} - 9 x + 18$ Hence factories the expression
(ii) (x+5) is a factor of $2 x^{3} + 5 x^{2} - 28 x - 15$ Hence factorise fthe expression $2 x^{3} + 5 x^{2} - 28 x - 18$ completely.
(iii) (3x+2) is a factor fo $3 x^{3} + 2 x^{2} - 3 x - 2.$ Hence factorise the expression
$3 x^{3} + 2 x^{2} - 3 x - 2$ completely