Given:
[tex](2x^3+4x^2-35x+15)\div (x-3)[/tex]
To find:
The quotient by using the synthetic division.
Solution:
We have,
[tex](2x^3+4x^2-35x+15)\div (x-3)[/tex]
Here,
Dividend = [tex](2x^3+4x^2-35x+15)[/tex]
Divisor = [tex]x-3[/tex]
The coefficient of dividend are [tex]2, 4, -35, 15[/tex]. Write the coefficients of the dividend on the top row and we need to use 3 as divisor for synthetic division. The synthetic division is show below:
[tex]3 | 2\quad \quad 4\quad \quad -35\quad \quad 15\\\quad{}\quad{} \quad \quad \ 6\quad \quad \ \ \ 30\quad -15\\\overline{\quad 2\quad \quad 10\quad \quad -5\quad \quad 0\ \ \ }[/tex]
The bottom row represents the coefficients of quotient but the last element of bottom row is the remainder.
Degree of dividend is 3 and degree of division is 1. So, the degree of quotient must be [tex]3-1=2[/tex].
The quotient is [tex]2x^2+10x-5[/tex] and the reminder is 0.
Therefore, the correct option is D.
