Answer :
To simplify the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)\)[/tex], follow these steps:
1. Combine Similar Terms:
- Cubic term ([tex]\(x^3\)[/tex]): The first polynomial has [tex]\(4x^3\)[/tex] and the second polynomial has [tex]\(3x^3\)[/tex]. Add these together:
[tex]\[4x^3 + 3x^3 = 7x^3\][/tex]
- Quadratic term ([tex]\(x^2\)[/tex]): The first polynomial has no [tex]\(x^2\)[/tex] term, which is equivalent to [tex]\(0x^2\)[/tex]. The second polynomial has [tex]\(-5x^2\)[/tex]. Add these together:
[tex]\[0x^2 - 5x^2 = -5x^2\][/tex]
- Linear term ([tex]\(x\)[/tex]): The first polynomial has [tex]\(6x\)[/tex] and the second polynomial has [tex]\(-5x\)[/tex]. Add these together:
[tex]\[6x - 5x = x\][/tex]
- Constant term: The first polynomial has [tex]\(-7\)[/tex], and the second polynomial has [tex]\(9\)[/tex]. Add these together:
[tex]\[-7 + 9 = 2\][/tex]
2. Write the Simplified Polynomial: After combining all like terms, you get:
[tex]\[7x^3 - 5x^2 + x + 2\][/tex]
3. Choose the Correct Answer: The expression simplifies to [tex]\(7x^3 - 5x^2 + x + 2\)[/tex], which corresponds to option B: [tex]\(7x^3 - 5x^2 + x + 2\)[/tex]. However, there might be an error in the options you provided, as option B in your list doesn't match exactly with what's calculated here. The closest match is option A: [tex]\(7x^3 - 5x^2 - x + 2\)[/tex], but note that the linear term should actually be [tex]\(x\)[/tex], not [tex]\(-x\)[/tex].
The correct representation of your simplified polynomial should be a match to either the options provided or it might require a re-evaluation of the given options. Please verify with the intended correct choice.
1. Combine Similar Terms:
- Cubic term ([tex]\(x^3\)[/tex]): The first polynomial has [tex]\(4x^3\)[/tex] and the second polynomial has [tex]\(3x^3\)[/tex]. Add these together:
[tex]\[4x^3 + 3x^3 = 7x^3\][/tex]
- Quadratic term ([tex]\(x^2\)[/tex]): The first polynomial has no [tex]\(x^2\)[/tex] term, which is equivalent to [tex]\(0x^2\)[/tex]. The second polynomial has [tex]\(-5x^2\)[/tex]. Add these together:
[tex]\[0x^2 - 5x^2 = -5x^2\][/tex]
- Linear term ([tex]\(x\)[/tex]): The first polynomial has [tex]\(6x\)[/tex] and the second polynomial has [tex]\(-5x\)[/tex]. Add these together:
[tex]\[6x - 5x = x\][/tex]
- Constant term: The first polynomial has [tex]\(-7\)[/tex], and the second polynomial has [tex]\(9\)[/tex]. Add these together:
[tex]\[-7 + 9 = 2\][/tex]
2. Write the Simplified Polynomial: After combining all like terms, you get:
[tex]\[7x^3 - 5x^2 + x + 2\][/tex]
3. Choose the Correct Answer: The expression simplifies to [tex]\(7x^3 - 5x^2 + x + 2\)[/tex], which corresponds to option B: [tex]\(7x^3 - 5x^2 + x + 2\)[/tex]. However, there might be an error in the options you provided, as option B in your list doesn't match exactly with what's calculated here. The closest match is option A: [tex]\(7x^3 - 5x^2 - x + 2\)[/tex], but note that the linear term should actually be [tex]\(x\)[/tex], not [tex]\(-x\)[/tex].
The correct representation of your simplified polynomial should be a match to either the options provided or it might require a re-evaluation of the given options. Please verify with the intended correct choice.
