Answered

IDNLearn.com makes it easy to find the right answers to your questions. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.

What is the sum of [tex]5x^2 + 3x - 7[/tex] and [tex]12x + 12[/tex]?

A. [tex]5x^2 + 15x + 5[/tex]

B. [tex]5x^2 + 15x + 19[/tex]

C. [tex]17x^2 + 3x + 5[/tex]

D. [tex]17x^2 + 15x + 12[/tex]

E. [tex]20x^4 + 5[/tex]

Sagot :

GinnyAnsweridn
To find the sum of the two polynomials [tex]\(5x^2 + 3x - 7\)[/tex] and [tex]\(12x + 12\)[/tex], follow these steps:

1. Align the polynomials by their terms: Make sure each polynomial is set up so that corresponding terms (constant terms, [tex]\(x\)[/tex] terms, [tex]\(x^2\)[/tex] terms, etc.) are aligned. For this problem, the polynomials are:

[tex]\[ 5x^2 + 3x - 7 \][/tex]
[tex]\[ 0x^2 + 12x + 12 \][/tex]

2. Perform the addition: Add the coefficients of corresponding terms. Arrange the polynomials like this and combine:

[tex]\[ (5x^2 + 3x - 7) + (0x^2 + 12x + 12) \][/tex]

- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 5x^2 + 0x^2 = 5x^2 \][/tex]

- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 3x + 12x = 15x \][/tex]

- Combine the constant terms:
[tex]\[ -7 + 12 = 5 \][/tex]

3. Write the resulting polynomial: After combining all the terms, the polynomial is:

[tex]\[ 5x^2 + 15x + 5 \][/tex]

From the options provided:

- [tex]\(5 x^2 + 15 x + 5\)[/tex]
- [tex]\(5 x^2 + 15 x + 19\)[/tex]
- [tex]\(17 x^2 + 3 x + 5\)[/tex]
- [tex]\(17 x^2 + 15 x + 12\)[/tex]
- [tex]\(20 x^4 + 5\)[/tex]

The correct answer is:

[tex]\[ 5 x^2 + 15 x + 5 \][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.