College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Question 2 of 45

Which of the following represents the sum of the polynomials below?

[tex]\[\left(6x^3 + 2x^2 + 9x\right) + \left(-2x^3 + 5x^2 + 3x\right)\][/tex]

A. [tex]\(4x^3 + 7x^2 + 12x\)[/tex]

B. [tex]\(4x^3 + 7x^2 + 6x\)[/tex]

C. [tex]\(8x^3 + 7x^2 + 12x\)[/tex]

D. [tex]\(4x^3 + 7x^2 + 12\)[/tex]

Answer :

To find the sum of the given polynomials [tex]\((6x^3 + 2x^2 + 9x) + (-2x^3 + 5x^2 + 3x)\)[/tex], follow these steps:

1. Identify the like terms in each polynomial.
- For [tex]\(x^3\)[/tex] terms: [tex]\(6x^3\)[/tex] and [tex]\(-2x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(2x^2\)[/tex] and [tex]\(5x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(9x\)[/tex] and [tex]\(3x\)[/tex]

2. Add the like terms together.
- For the [tex]\(x^3\)[/tex] terms: [tex]\(6x^3 + (-2x^3) = 6x^3 - 2x^3 = 4x^3\)[/tex]
- For the [tex]\(x^2\)[/tex] terms: [tex]\(2x^2 + 5x^2 = 7x^2\)[/tex]
- For the [tex]\(x\)[/tex] terms: [tex]\(9x + 3x = 12x\)[/tex]

3. Combine these results to form the resulting polynomial sum.
- Which gives us: [tex]\(4x^3 + 7x^2 + 12x\)[/tex]

Thus, the sum of the polynomials [tex]\((6x^3 + 2x^2 + 9x)\)[/tex] and [tex]\((-2x^3 + 5x^2 + 3x)\)[/tex] is:

Answer:
A. [tex]\(4x^3 + 7x^2 + 12x\)[/tex]