Question

(2x45x²+3) ÷ (x² + 2)

Answer 1

`\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.