Question

use synthetic division to simplify \\(\frac{x^4 - 22x^2 + 15x}{x + 5}\\).
write your answer in the form \\(q(x) + \frac{r}{d(x)}), where \\(q(x)\\) is a polynomial, \\(r\\) is an integer, and \\(d(x)\\) is a linear polynomial. simplify any fractions.

Explanation:

-5: $0$. Add to last coefficient: $0+0=0$.

Step4: Form quotient and remainder

Quotient: $x^3 -5x^2 +3x$, Remainder: $0$

Step5: Write final form

$x^3 -5x^2 +3x + \frac{0}{x+5}$

Answer:

-5: $0$. Add to last coefficient: $0+0=0$.

Step4: Form quotient and remainder

Quotient: $x^3 -5x^2 +3x$, Remainder: $0$

Step5: Write final form

$x^3 -5x^2 +3x + \frac{0}{x+5}$