SaiBook.us Algebra

Home Course Section

Schedule Admission Social

Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Synthetic division

Grade: 8-a Lesson: S1-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Using synthetic division, determine the remainder when the polynomial \$ 2x^5 - 3x^4 + x^3 − 4x^2 + 3x − 1 \$ is divided by the binomial \$x − 2\$.
2	Step	Given polynomial:	\$ 2x^5 - 3x^4 + x^3 − 4x^2 + 3x − 1 \$
3	Step	Write down the coefficients of the polynomial	Coefficients: 2, -3, 1, -4, 3, -1
4	Step	Write the root of the divisor inside the division box	Divisor root: 2
5	Step	Draw a horizontal line under the coefficients.
6	Step	Bring down the first coefficient (2) below the horizontal line.
7	Step	Multiply the divisor root (2) by the number you just brought down (2), and write the result beneath the next coefficient (-3)	\$ 2 \times 2 \$ = 4 Write 4 beneath -3
8	Step	Add the two numbers diagonally downward, and write the sum below the line	4 + (-3) = 1 Write 1 below 1
9	Step	Repeat these steps until you’ve gone through all the coefficients
10	Step	The number on the bottom right corner is the remainder	Remainder: 13
11	Step	So, when the polynomial \$ 2x^5 - 3x^4 + x^3 − 4x^2 + 3x − 1 \$ is divided by \$x - 2\$, the remainder is 13.
12	Choice.A	This option doesn’t match the remainder we obtained, which is 13	7
13	Choice.B	This option suggests a remainder of 14. However, our calculation using synthetic division yielded a remainder of 13. So, this option is incorrect	14
14	Choice.C	This option matches the remainder we obtained using synthetic division, which is 13. Therefore, this option is correct	13
15	Choice.D	This option suggests a remainder of 6. However, our calculation using synthetic division yielded a remainder of 13. So, this option is incorrect	6
16	Answer	Option	C
17	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Using synthetic division, determine the remainder when the polynomial \$ 2x^5 - 3x^4 + x^3 − 4x^2 + 3x − 1 \$ is divided by the binomial \$x − 2\$.

Step

Given polynomial:

\$ 2x^5 - 3x^4 + x^3 − 4x^2 + 3x − 1 \$

Step

Write down the coefficients of the polynomial

Coefficients: 2, -3, 1, -4, 3, -1

Step

Write the root of the divisor inside the division box

Divisor root: 2

Step

Draw a horizontal line under the coefficients.

Step

Bring down the first coefficient (2) below the horizontal line.

Step

Multiply the divisor root (2) by the number you just brought down (2), and write the result beneath the next coefficient (-3)

\$ 2 \times 2 \$ = 4
Write 4 beneath -3

Step

Add the two numbers diagonally downward, and write the sum below the line

4 + (-3) = 1
Write 1 below 1

Step

Repeat these steps until you’ve gone through all the coefficients

Step

The number on the bottom right corner is the remainder

Remainder: 13

Step

So, when the polynomial \$ 2x^5 - 3x^4 + x^3 − 4x^2 + 3x − 1 \$ is divided by \$x - 2\$, the remainder is 13.

Choice.A

This option doesn’t match the remainder we obtained, which is 13

Choice.B

This option suggests a remainder of 14. However, our calculation using synthetic division yielded a remainder of 13. So, this option is incorrect

Choice.C

This option matches the remainder we obtained using synthetic division, which is 13. Therefore, this option is correct

Choice.D

This option suggests a remainder of 6. However, our calculation using synthetic division yielded a remainder of 13. So, this option is incorrect

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?