Answer :
To find the polynomial representing the sum of [tex]\((4x^2 + 6)\)[/tex] and [tex]\((2x^2 + 6x + 3)\)[/tex], follow these steps:
1. Identify and Combine Like Terms:
- For [tex]\(x^2\)[/tex] terms: Add the coefficients of the [tex]\(x^2\)[/tex] terms from both polynomials.
- The first polynomial has [tex]\(4x^2\)[/tex] and the second has [tex]\(2x^2\)[/tex].
- Combine them: [tex]\(4x^2 + 2x^2 = 6x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: Look at the coefficients of the [tex]\(x\)[/tex] terms.
- Only the second polynomial has an [tex]\(x\)[/tex] term, which is [tex]\(6x\)[/tex].
- Thus, it remains [tex]\(6x\)[/tex].
- For Constant terms: Add the constant terms from both polynomials.
- The first polynomial has [tex]\(6\)[/tex] and the second has [tex]\(3\)[/tex].
- Combine them: [tex]\(6 + 3 = 9\)[/tex].
2. Write the Resulting Polynomial:
The sum of the polynomials is [tex]\(6x^2 + 6x + 9\)[/tex].
Therefore, the polynomial that represents the sum is [tex]\(6x^2 + 6x + 9\)[/tex]. This matches option B in the given choices.
1. Identify and Combine Like Terms:
- For [tex]\(x^2\)[/tex] terms: Add the coefficients of the [tex]\(x^2\)[/tex] terms from both polynomials.
- The first polynomial has [tex]\(4x^2\)[/tex] and the second has [tex]\(2x^2\)[/tex].
- Combine them: [tex]\(4x^2 + 2x^2 = 6x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: Look at the coefficients of the [tex]\(x\)[/tex] terms.
- Only the second polynomial has an [tex]\(x\)[/tex] term, which is [tex]\(6x\)[/tex].
- Thus, it remains [tex]\(6x\)[/tex].
- For Constant terms: Add the constant terms from both polynomials.
- The first polynomial has [tex]\(6\)[/tex] and the second has [tex]\(3\)[/tex].
- Combine them: [tex]\(6 + 3 = 9\)[/tex].
2. Write the Resulting Polynomial:
The sum of the polynomials is [tex]\(6x^2 + 6x + 9\)[/tex].
Therefore, the polynomial that represents the sum is [tex]\(6x^2 + 6x + 9\)[/tex]. This matches option B in the given choices.
