Question

Use synthetic division to solve (2x3+4x2 – 35x+15) +(x-3). What is the quotient?

Answer 1

Given:

$(2x^3+4x^2-35x+15)\div (x-3)$

To find:

The quotient by using the synthetic division.

Solution:

We have,

$(2x^3+4x^2-35x+15)\div (x-3)$

Here,

Dividend = $(2x^3+4x^2-35x+15)$

Divisor = $x-3$

The coefficient of dividend are $2, 4, -35, 15$. 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:

$3 | 2\quad \quad 4\quad \quad -35\quad \quad 15\\\quad{}\quad{} \quad \quad \ 6\quad \quad \ \ \ 30\quad -15\\\overline{\quad 2\quad \quad 10\quad \quad -5\quad \quad 0\ \ \ }$

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 $3-1=2$.

The quotient is $2x^2+10x-5$ and the reminder is 0.

Therefore, the correct option is D.