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(2x45x²+3) ÷ (x² + 2)

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Answer:


\frac{{2x^4 + 5x^2 + 3}}{{x^2 + 2}} = \frac{{(2x^2 + 3)(x^2 + 1)}}{{x^2 + 2}}

Explanation:

To simplify the expression
\frac{{2x^4 + 5x^2 + 3}}{{x^2 + 2}}, we can factor the numerator and then perform the division.

First, let's factor the numerator:


2x^4 + 5x^2 + 3

This expression looks like a quadratic in terms
\sf \:\:of\: x^2. \:Let's\: denote \:y = x^2, so we have:


2y^2 + 5y + 3

Factoring this quadratic equation:


2y^2 + 5y + 3 \\\\ 2y^2 + 2y + 3y + 3 \\\\2y(y + 1) + 3(y + 1) \\\\ (2y + 3)(y + 1)

Now, substitute
y = x^2 back:


(2x^2 + 3)(x^2 + 1)

So, the expression becomes:


\frac{{2x^4 + 5x^2 + 3}}{{x^2 + 2}} = \frac{{(2x^2 + 3)(x^2 + 1)}}{{x^2 + 2}}

This is the simplified form of the expression.

User Carrutherji
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