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Step-5

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	Solve the following polynomials \$(2x^3 - 3x + 5) / (x - 4)\$.
2	Step	The polynomials expression is	\$(2x^3 - 3x + 5) / (x - 4)\$
3	Step	First perform long division to divide	$5$
4	Step	So, the result of the division is \$2x^2 + 8x + 29\$ with a remainder of 121.
5	Step	Quotient and Remainder: So, the polynomial can be written as	\$(2x^3 - 3x + 5) / (x - 4) = 2x^2 + 8x + 29 + (121) /(x - 4)\$
6	Choice.A	Option A is accurate as it aligns with the outcome derived from the polynomial division	\$2x^2 + 8x + 29 + 121/(x - 4)\$
7	Choice.B	The denominator should be x − 4, not x + 4, so this is incorrect	\$2x^2 + 8x + 29 + 121/(x + 4)\$
8	Choice.C	The sign before the remainder should be positive since the remainder is 121, so this is incorrect	\$2x^2 + 8x - 29 - 121/(x - 4)\$
9	Choice.D	Option D is incorrect because it has the wrong sign for the coefficient of the x term	\$2x^2 - 8x - 29 + 121/(x - 4)\$
10	Answer	Option	A
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve the following polynomials \$(2x^3 - 3x + 5) / (x - 4)\$.

Step

The polynomials expression is

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

Step

First perform long division to divide

$5$

Step

So, the result of the division is \$2x^2 + 8x + 29\$ with a remainder of 121.

Step

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

\$(2x^3 - 3x + 5) / (x - 4) = 2x^2 + 8x + 29 + (121) /(x - 4)\$

Choice.A

Option A is accurate as it aligns with the outcome derived from the polynomial division

\$2x^2 + 8x + 29 + 121/(x - 4)\$

Choice.B

The denominator should be x − 4, not x + 4, so this is incorrect

\$2x^2 + 8x + 29 + 121/(x + 4)\$

Choice.C

The sign before the remainder should be positive since the remainder is 121, so this is incorrect

\$2x^2 + 8x - 29 - 121/(x - 4)\$

Choice.D

Option D is incorrect because it has the wrong sign for the coefficient of the x term

\$2x^2 - 8x - 29 + 121/(x - 4)\$

Answer

Option

Sumup

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