Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Choose the correct sum of the polynomials

[tex]\[
\left(4x^3 - 2x - 9\right) + \left(2x^3 + 5x + 3\right).
\][/tex]

A. [tex]\(6x^3 - 3x - 6\)[/tex]
B. [tex]\(2x^3 - 7x - 12\)[/tex]
C. [tex]\(6x^3 + 3x - 6\)[/tex]
D. [tex]\(2x^3 + 3x - 3\)[/tex]


Sagot :

To find the sum of the given polynomials [tex]\((4x^3 - 2x - 9)\)[/tex] and [tex]\((2x^3 + 5x + 3)\)[/tex], we will add the corresponding coefficients of the same powers of [tex]\(x\)[/tex]. Here’s how you can do it step-by-step:

1. Identify and list the coefficients of each power of [tex]\(x\)[/tex]:

For the first polynomial [tex]\((4x^3 - 2x - 9)\)[/tex]:
- [tex]\(x^3\)[/tex] term: [tex]\(4\)[/tex]
- [tex]\(x^2\)[/tex] term: [tex]\(0\)[/tex] (since there is no [tex]\(x^2\)[/tex] term, the coefficient is [tex]\(0\)[/tex])
- [tex]\(x\)[/tex] term: [tex]\(-2\)[/tex]
- Constant term: [tex]\(-9\)[/tex]

For the second polynomial [tex]\((2x^3 + 5x + 3)\)[/tex]:
- [tex]\(x^3\)[/tex] term: [tex]\(2\)[/tex]
- [tex]\(x^2\)[/tex] term: [tex]\(0\)[/tex] (since there is no [tex]\(x^2\)[/tex] term, the coefficient is [tex]\(0\)[/tex])
- [tex]\(x\)[/tex] term: [tex]\(5\)[/tex]
- Constant term: [tex]\(3\)[/tex]

2. Add the coefficients of the corresponding terms:

- For [tex]\(x^3\)[/tex] terms: [tex]\(4 + 2 = 6\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(0 + 0 = 0\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-2 + 5 = 3\)[/tex]
- For the constant terms: [tex]\(-9 + 3 = -6\)[/tex]

3. Combine these results to form the polynomial:

The resulting polynomial after adding the coefficients is:
[tex]\(6x^3 + 0x^2 + 3x - 6\)[/tex]

Simplifying the polynomial expression (where [tex]\(0x^2\)[/tex] is typically omitted):
[tex]\(6x^3 + 3x - 6\)[/tex]

Therefore, the correct sum of the polynomials [tex]\(\left(4x^3 - 2x - 9\right) + \left(2x^3 + 5x + 3\right)\)[/tex] is:

[tex]\[6x^3 + 3x - 6\][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{6x^3 + 3x - 6} \][/tex]