Question

Simplify the following polynomial expression.

(5x^4 - 9x^3 + 7x - 1) + (-8x^4 +
4x^2– 3x + 2) - (-4x^3 + 5x - 1)(2x -7)
A 5x^4 - 37x^3 - 6x^2 + 41x - 6
B. 11x^4- 21x^3 + 14x^2 + 33x-8
C. 11x^4- 21x^3 + 14x^2 + 33x- 6
D. 5x^4– 37x^3- 6x^2 + 4x - 8

Answer 1

`5x^4- 37x^3-6x^2+ 41x-6`

Explanation:

simplify the following expression:

`(5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2-3x + 2) - (-4x^3 + 5x - 1)(2x -7)`

Expand
`(-4x^3 + 5x - 1)(2x -7)`

`\implies -8x^4 +28x^3+10x^2-35x-2x+7\\\\\implies -8x^4 +28x^3+10x^2-37x+7\\`

Therefore:

`(5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2- 3x + 2)-(-8x^4 +28x^3+10x^2-37x+7)`

Group and combine like terms:

`5x^4 -8x^4- 9x^3 +4x^2+ 7x - 3x- 1 + 2-(-8x^4 +28x^3+10x^2-37x+7)\\\\\implies -3x^4- 9x^3 +4x^2+ 4x +1-(-8x^4 +28x^3+10x^2-37x+7)`

Apply the distributive rule:
`-(-a+b)=a-b`

`\implies -3x^4- 9x^3 +4x^2+ 4x +1+8x^4-28x^3-10x^2+37x-7`

Group and combine like terms:

`\implies -3x^4+8x^4- 9x^3 -28x^3+4x^2-10x^2+ 4x+37x +1-7\\\\\implies 5x^4- 37x^3-6x^2+ 41x-6`

Answer 2

A.
`5x^4 - 37x^3 - 6x^2 + 41x - 6`

step-by-step-explanation:

• 
  `(5x^4 - 9x^3 + 7x - 1) + (-8x^4 +4x^2- 3x + 2) - (-4x^3 + 5x - 1)(2x -7)`

• 
  `(5x^4 - 9x^3 + 7x - 1) -8x^4 +4x^2- 3x + 2 - (-8x^4+28x^3+10x^2-37x+7)`
• 
  `5x^4 - 9x^3 + 7x - 1-8x^4 +4x^2- 3x + 2 +8x^4-28x^3-10x^2+37x-7`
• 
  `5x^4 -8x^4 + 8x^4 -9x^3 -28x^3 +4x^2 -10x^2 +37x +7x -3x -7 -1 +2`
• 
  `5x^4 - 37x^3 - 6x^2 + 41x - 6`