Question

Divide using synthetic division, and write a summary statement in fraction form. 3x^5+4x^4+2x^2-1/x+2.

Answer 1

Hi, Tyler, and welcome to OpenStudy!!

While your question is clear to someone familiar with synthetic and long division, it'd be better if you'd enclose your divisor (x+2) within parentheses.

If we want to carry out this division using synthetic division, the first step is to take that divisor, x+2, and extract the possible root -2. Be sure you understand what's happening here; if you don't, let's talk further.

Then, setting up your synthetic div., we steal the coefficients from your dividend (3x^5+4x^4+2x^2-1):

-2 | 3 4 0 2 0 -1 Can you explain where those two zeros came from??

-------------------
3 Bring that first coefficient (3) down to underneath the
line. Multiply that 3 by the divisor (-2), and write
the product (-6) under the 4.


-2 | 3 4 0 2 0 -1
-6
-------------------
3 -2


Can you now finish this synthetic division?