110k views
2 votes
Hi. I need help with these questions.
See image for question.


Hi. I need help with these questions. See image for question. ​-example-1
User Esmee
by
7.4k points

2 Answers

6 votes

Explanation:

Given

f(x) = 4x³ + 3x² - 2x - 1

Divide it by the following:

(a) 2x + 1

4x³ + 3x² - 2x - 1 =

(4x³ + 2x²) + (x² + 1/2x) - (5/2x + 5/4) + 1/4 =

2x²(2x+1) + 1/2x(2x + 1) - 5/4(2x + 1) + 1/4 =

(2x + 1)(2x² + 1/2x - 5/4) + 1/4

Quotient = 2x² + 1/2x - 5/4

Remainder = 1/4

(b) 2x - 3

4x³ + 3x² - 2x - 1 =

(4x³ - 6x²) + (9x² - 13.5x) + (11.5x - 17.25) + 16.25 =

(2x -3)(2x² + 4.5x + 5.75) + 16.25

Quotient = 2x² + 4.5x + 5.75

Remainder = 16.25

(c) 4x - 1

4x³ + 3x² - 2x - 1 =

(4x³ - x²) + (4x² - x) - (2x - 1/2) - 3/2 =

(4x - 1)(x² + x - 1/2) - 3/2

Quotient = x² + x - 1/2

Remainder = - 3/2

(d) x + 2

4x³ + 3x² - 2x - 1 =

(4x³ + 8x²) - (5x² + 10x) + (8x + 16) - 17 =

(x + 2)(4x² - 5x + 8) - 17

Quotient = 4x² - 5x + 8

Remainder = - 17

User Jpobst
by
8.3k points
4 votes

Explanation:

Given

  • f(x) = 4x³ + 3x² - 2x - 1

Divide it by the following:

(a) 2x + 1

  • 4x³ + 3x² - 2x - 1 =
  • (4x³ + 2x²) + (x² + 1/2x) - (5/2x + 5/4) + 1/4 =
  • 2x²(2x+1) + 1/2x(2x + 1) - 5/4(2x + 1) + 1/4 =
  • (2x + 1)(2x² + 1/2x - 5/4) + 1/4

Quotient = 2x² + 1/2x - 5/4

Remainder = 1/4

(b) 2x - 3

  • 4x³ + 3x² - 2x - 1 =
  • (4x³ - 6x²) + (9x² - 13.5x) + (11.5x - 17.25) + 16.25 =
  • (2x -3)(2x² + 4.5x + 5.75) + 16.25

Quotient = 2x² + 4.5x + 5.75

Remainder = 16.25

(c) 4x - 1

  • 4x³ + 3x² - 2x - 1 =
  • (4x³ - x²) + (4x² - x) - (2x - 1/2) - 3/2 =
  • (4x - 1)(x² + x - 1/2) - 3/2

Quotient = x² + x - 1/2

Remainder = - 3/2

(d) x + 2

  • 4x³ + 3x² - 2x - 1 =
  • (4x³ + 8x²) - (5x² + 10x) + (8x + 16) - 17 =
  • (x + 2)(4x² - 5x + 8) - 17

Quotient = 4x² - 5x + 8

Remainder = - 17

User ChrisAdkin
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories