Middle School

What is the sum of \((2x^4 + 5x^3 - 8x^2 - x + 10)\) and \((8x^4 - 4x^3 + x^2 - x + 2)\)?

A) \(10x^4 + x^3 - 9x^2 - 2x + 12\)

B) \(10x^4 + 9x^3 - 7x^2 - 2x + 12\)

C) \(10x^4 + x^3 - 9x^2 + 12\)

D) \(10x^4 + x^3 - 7x^2 - 2x + 12\)

Answer :

Option D: [tex]10x^4+x^3-7x^2-2x+12[/tex] is the right answer

Step-by-step explanation:

Given polynomials are:

[tex]P_1 : 2x^4+5x^3-8x^2-x+10\\P_2: 8x^4-4x^3+x^2-x+2[/tex]

We have to find the sum of polynomials

So,

[tex]S = P_1+P_2\\= (2x^4+5x^3-8x^2-x+10) + (8x^4-4x^3+x^2-x+2)\\=2x^4+5x^3-8x^2-x+10+8x^4-4x^3+x^2-x+2\\[/tex]

Combining like terms

[tex]=2x^2+8x^4+5x^2-4x^3-8x^2+x^2-x-x+10+2\\= 10x^4+x^3-7x^2-2x+12[/tex]

Hence,

Option D: [tex]10x^4+x^3-7x^2-2x+12[/tex] is the right answer

Keywords: Polynomials, sum

Learn more about polynomials at:

  • brainly.com/question/2116906
  • brainly.com/question/2131336

#LearnwithBrainly

Answer:

D

Step-by-step explanation:

hope it helps

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