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]
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]
