The product of two expressions is $x^{5} + x^{3} + x$ .If one of them is $x^{2} + x + 1$ , find the other.

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Solution

Let the other equation be $y$
According to question
$y \times (x^{2} + x + 1) = x^{5} + x^{3} + x$

$∵ y = \frac{x^{5} + x^{3} + x}{x^{2} + x + 1}$
Now By using the long division method
As shown in the figure
hence on solving the equation the other expression is $x^{3} - x^{2} + x$ .

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The product of two expressions is x5+x3+x.If one of them is x2+x+1, find the other.

Let the other equation be yAccording to questiony×(x2+x+1)=x5+x3+x ∵y=x5+x3+xx2+x+1 Now By using the long division method As shown in the figure hence on solving the equation the other expression is x3−x2+x.

The product of two expressions is $x^{5} + x^{3} + x$ .If one of them is $x^{2} + x + 1$ , find the other.

Let the other equation be $y$
According to question
$y \times (x^{2} + x + 1) = x^{5} + x^{3} + x$

$∵ y = \frac{x^{5} + x^{3} + x}{x^{2} + x + 1}$
Now By using the long division method
As shown in the figure
hence on solving the equation the other expression is $x^{3} - x^{2} + x$ .