College

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]