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2

5.3.3 Quiz: Synthetic Division

Question 5 of 10

2 Points

What is the remainder in the synthetic division problem below?

11 2 -3 3

O

A. 5

OB. 4

O

c. 6

OD. 3

Sagot :

MrRoyal

Answer:

[tex]Remainder = 3[/tex]

Step-by-step explanation:

Given

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

Required

Determine the remainder

Write down the first digit i.e. 1. So, we have:

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

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

  [tex]|\ 1[/tex]

Multiply that 1 by the divisor (1) i.e. [tex]1 * 1 = 1[/tex]

Write down the result under the next digit i.e. (under 2)

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

        [tex]1[/tex]

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

  [tex]|\ 1[/tex]

Sum 2 and 1 i.e [tex]2 + 1 = 3[/tex]

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

        [tex]1[/tex]

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

  [tex]|\ 1\ \ 3[/tex]  

Multiply that 3 by the divisor (1) i.e. [tex]1 * 3 = 3[/tex]

Write down the result under the next digit i.e. (under -3)

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

        [tex]1[/tex]       [tex]3[/tex]

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

  [tex]|\ 1\ \ 3[/tex]  

Sum -3 and 3 i.e [tex]-3 + 3 = 0[/tex]

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

        [tex]1[/tex]       [tex]3[/tex]

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

  [tex]|\ 1\ \ 3\ \ \ 0[/tex]

 

Multiply that 0 by the divisor (1) i.e. [tex]1 * 0 = 0[/tex]

Write down the result under the next digit i.e. (under 3)

[tex]1\ |\ 1\ \ 2\ \ -3\ \ 3[/tex]

        [tex]1[/tex]       [tex]3[/tex]   [tex]0[/tex]

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

  [tex]|\ 1\ \ 3\ \ \ 0[/tex]

Sum 3 and 0 i.e [tex]3 + 0 = 3[/tex]

Since there is no other computation to do, the result of the last sum is the remainder.

So:

[tex]Remainder = 3[/tex]

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