Question

the product of two expression is x to the power 5 plus x qube plus x if one of them is X square + X + 1 find the other

Answer 1

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Answer 2

The other expression is $(x^{3} - x^{2} + x)$

Step-by-step explanation:

The expression of the product is given to be $x^{5} + x^{3} + 1$ and this is the product of two expressions, one of which is (x² + x + 1) and we have to find the other expression.

Now, $x^{5} + x^{3} + 1$

= $x^{5} + x^{4} + x^{3} - x^{4} - x^{3} - x^{2} + x^{3} + x^{2} + x$

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

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

Therefore, the other expression is $(x^{3} - x^{2} + x)$ (Answer)