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]
