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Title: Dividing polynomials

Grade: 8-a Lesson: S1-L3

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

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Divide the following polynomials \$ (5x^3 + 4x^2 + x + 3) ÷ (x^2 + 2x - 1)\$.
2	Step	The given polynomials expression is	\$ (5x^3 + 4x^2 + x + 3) ÷ (x^2 + 2x -1)\$
3	Step	$4$
4	Step	So, the result of the division is \$5x^3 + 4x^2 + x+ 3\$ with a remainder of 17x - 3.
5	Step	Quotient and Remainder: So, the polynomial can be written as	\$5x - 6 + (17x - 3)/ (x^2 + 2x - 1)\$
6	Choice.A	Wrong: The constant term in the remainder should be − 3 instead of + 3	\$5x - 6 + (17x + 3) / (x^2 + 2x +1)\$
7	Choice.B	Wrong: The constant term in the quotient should be - 6 instead of + 6	\$5x + 6 + (17x - 3) / (x^2 + 2x +1)\$
8	Choice.C	Option C is correct because it follows the correct form of the division	\$5x - 6 + (17x - 3) / (x^2 + 2x +1)\$
9	Choice.D	The signs in the quotient differ, yielding a remainder of 17x, not -17x as stated wrongly	\$- 5x + 6 + (-17x - 3) / (x^2 + 2x +1)\$
10	Answer	Option	C
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Divide the following polynomials \$ (5x^3 + 4x^2 + x + 3) ÷ (x^2 + 2x - 1)\$.

Step

The given polynomials expression is

\$ (5x^3 + 4x^2 + x + 3) ÷ (x^2 + 2x -1)\$

Step

$4$

Step

So, the result of the division is \$5x^3 + 4x^2 + x+ 3\$ with a remainder of 17x - 3.

Step

Quotient and Remainder: So, the polynomial can be written as

\$5x - 6 + (17x - 3)/ (x^2 + 2x - 1)\$

Choice.A

Wrong: The constant term in the remainder should be − 3 instead of + 3

\$5x - 6 + (17x + 3) / (x^2 + 2x +1)\$

Choice.B

Wrong: The constant term in the quotient should be - 6 instead of + 6

\$5x + 6 + (17x - 3) / (x^2 + 2x +1)\$

Choice.C

Option C is correct because it follows the correct form of the division

\$5x - 6 + (17x - 3) / (x^2 + 2x +1)\$

Choice.D

The signs in the quotient differ, yielding a remainder of 17x, not -17x as stated wrongly

\$- 5x + 6 + (-17x - 3) / (x^2 + 2x +1)\$

Answer

Option

Sumup

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