Answer:
[tex]\frac{6x^3 \ + \ 19x^2 \ + \ 17x \ + \ 3}{2x \ + \ 3} \ = \ 3x^2 \ + \ 5x \ + \ 1[/tex]
Step-by-step explanation:
Given;
F(x) = 6x³ + 19x² + 17x + 3
Factor of F(x) = 2x + 3
Using long division method;
3x² + 5x + 1
------------------------------------
2x + 3 √ 6x³ + 19x² + 17x + 3
- (6x³ + 9x²)
----------------------------------------
10x² + 17x + 3
- (10x² + 15x)
-------------------------------
2x + 3
- (2x + 3)
---------------
0
[tex]Thus, \frac{6x^3 \ + \ 19x^2 \ + \ 17x \ + \ 3}{2x \ + \ 3} \ = 3x^2 \ + \ 5x \ + \ 1[/tex]
