Question

Could you show me how to divide x^3 + 2x^2 + x + 2 by x^2 + 1

Answer 1

Answer:

$x+2$

Step-by-step explanation:

For this division we can first use factoring of the numerator, then eliminate the common factors.

$\frac{x^{3} +2x^{2} +x+2}{x^{2}+1 }$

Factoring the numerator by the term grouping method

$\frac{x^{2} (x+2)+(x+2) }{x^{2} +1}$

$\frac{(x^{2} +1)(x+2)}{x^{2} +1}$

removed terms

$(x+2)$