A student is trying to use long division (at the right) to solve the following (3x³ – 4x? – x + 1) + (x + 1). What value should go in the box next? 3x x+1)3x - 4x - x+1 -(3x +3x*) 7x a. - 2x с. - 7x 2х d. 7x A В C
A student is trying to use long division (at the right) to solve the following (3x³ – 4x? – x + 1) + (x + 1). What value should go in the box next? 3x x+1)3x - 4x - x+1 -(3x +3x*) 7x a. - 2x с. - 7x 2х d. 7x A В C
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Long Division of Polynomials: Problem Solving**
**Instructions:**
Read carefully and respond accordingly.
---
A student is trying to use long division to solve the following polynomial division: \((3x^3 - 4x^2 - x + 1) \div (x + 1)\). Determine what value should go in the box next in the division process.
**Current Step in Long Division:**
1. Divide the first term of the dividend by the first term of the divisor: \(\frac{3x^3}{x} = 3x^2\).
2. Multiply \(3x^2\) by the whole divisor: \(3x^2 \times (x + 1) = 3x^3 + 3x^2\).
3. Subtract this product from the original dividend:
\[
\begin{align*}
&(3x^3 - 4x^2 - x + 1) \\
&- (3x^3 + 3x^2) = -7x^2 - x \\
\end{align*}
\]
**Options:**
- a. \(-2x\)
- b. \(2x\)
- c. \(-7x\)
- d. \(7x\)
**Possible Answers:**
Select the appropriate value for the box in the long division process by choosing one of the options (A, B, C, D) that correctly continues the subtraction step in the polynomial division.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c587c1-d88f-4e00-9baa-33dad02673fa%2F2f36e9e4-df68-4012-856a-66f20aed303a%2Ft0r2meq_processed.png&w=3840&q=75)
Transcribed Image Text:**Long Division of Polynomials: Problem Solving**
**Instructions:**
Read carefully and respond accordingly.
---
A student is trying to use long division to solve the following polynomial division: \((3x^3 - 4x^2 - x + 1) \div (x + 1)\). Determine what value should go in the box next in the division process.
**Current Step in Long Division:**
1. Divide the first term of the dividend by the first term of the divisor: \(\frac{3x^3}{x} = 3x^2\).
2. Multiply \(3x^2\) by the whole divisor: \(3x^2 \times (x + 1) = 3x^3 + 3x^2\).
3. Subtract this product from the original dividend:
\[
\begin{align*}
&(3x^3 - 4x^2 - x + 1) \\
&- (3x^3 + 3x^2) = -7x^2 - x \\
\end{align*}
\]
**Options:**
- a. \(-2x\)
- b. \(2x\)
- c. \(-7x\)
- d. \(7x\)
**Possible Answers:**
Select the appropriate value for the box in the long division process by choosing one of the options (A, B, C, D) that correctly continues the subtraction step in the polynomial division.
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