Show how you will find the remainder when 2x^2 + 5x – 3 is divided x + 3 by using synthetic division.

Given:

Dividend =

Divisor =

To find:

The remainder by using the synthetic division.

Solution:

We have,

Dividend =

The coefficients of dividend are 2, 5, -3. Write these elements in the top row of synthetic division.

Divisor =

The value of divisor is 0 at . So, write -3 on the left side of division.

Write down the first coefficient of dividend in bottom row, then multiply it by -3 and write the result below the next coefficient of dividend then add the coefficient and write the result in bottom row, then repeat the steps up-to last coefficient.

-3    |        2          5         -3

      |                    -6         3

------------------------------------------

               2         -1           0

-----------------------------------------

Here, the first two elements of the bottom row represent the coefficient of quotient and last element represent the remainder.

Therefore, the remainder is 0.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

c is the correct answer

step-by-step explanation: