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Lesson Example Discussion Quiz: Class Homework

Step-1

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	Divide the polynomial \$ 2x^2 - 3x + 1\$ by the binomial \$(x - 1)\$.
2	Step	The given polynomials are	\$ 2x^2 - 3x + 1\$ \$(x - 1)\$
3	Step	Identify the coefficients of the polynomial Identify the root from the divisor \$x − 1\$, which is 1 (opposite the sign of the constant in the binomial)	2, -3, 1 x - 1 = 0 x = 1
4	Step	Write down the coefficients of the polynomial and the root:	$1a$
5	Step	Bring down the first coefficient 2 directly under the line	$1b$
6	Step	Multiply the root 1 by the number you just brought down (2), place this number under the next coefficient (-3), and add to get the new number to bring down	$1c$
7	Step	The numbers on the bottom line after synthetic division are the coefficients of the quotient and the remainder Quotient: 2x − 1 Remainder: 0	$1d$
8	Choice.A	This option matches the correct result obtained from synthetic division. It states that the quotient polynomial is 2x − 1 and there is no remainder	Quotient: 2x − 1 with Remainder: 0
9	Choice.B	This option suggests that the quotient polynomial is 2x − 5 and there is a remainder of 4. However, this is not consistent with the synthetic division result we obtained	Quotient: 2x − 5 with Remainder: 4
10	Choice.C	This option correctly identifies the quotient polynomial as 2x − 1, but it suggests there is a remainder of 2. However, our synthetic division result showed a remainder of 0	Quotient: 2x − 1 with Remainder: 2
11	Choice.D	This option suggests that the quotient polynomial is 2x + 1 and there is a remainder of -2. Again, this is not consistent with the synthetic division result we obtained	Quotient: 2x + 1 with Remainder: -2
12	Answer	Option	A
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Divide the polynomial \$ 2x^2 - 3x + 1\$ by the binomial \$(x - 1)\$.

Step

The given polynomials are

\$ 2x^2 - 3x + 1\$
\$(x - 1)\$

Step

Identify the coefficients of the polynomial
Identify the root from the divisor \$x − 1\$, which is 1 (opposite the sign of the constant in the binomial)

2, -3, 1

x - 1 = 0
x = 1

Step

Write down the coefficients of the polynomial and the root:

$1a$

Step

Bring down the first coefficient 2 directly under the line

$1b$

Step

Multiply the root 1 by the number you just brought down (2), place this number under the next coefficient (-3), and add to get the new number to bring down

$1c$

Step

The numbers on the bottom line after synthetic division are the coefficients of the quotient and the remainder
Quotient: 2x − 1
Remainder: 0

$1d$

Choice.A

This option matches the correct result obtained from synthetic division. It states that the quotient polynomial is 2x − 1 and there is no remainder

Quotient: 2x − 1 with Remainder: 0

Choice.B

This option suggests that the quotient polynomial is 2x − 5 and there is a remainder of 4. However, this is not consistent with the synthetic division result we obtained

Quotient: 2x − 5 with Remainder: 4

Choice.C

This option correctly identifies the quotient polynomial as 2x − 1, but it suggests there is a remainder of 2. However, our synthetic division result showed a remainder of 0

Quotient: 2x − 1 with Remainder: 2

Choice.D

This option suggests that the quotient polynomial is 2x + 1 and there is a remainder of -2. Again, this is not consistent with the synthetic division result we obtained

Quotient: 2x + 1 with Remainder: -2

Answer

Option

Sumup

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