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Answer :
To find the sum of the two polynomials, we need to add the corresponding coefficients of the polynomials together. Here's how to do it step-by-step:
We have the following polynomials:
1. [tex]\( 4x^3 + 6x^2 + 2x - 3 \)[/tex]
2. [tex]\( 3x^3 + 3x^2 - 5x - 5 \)[/tex]
Now let's add them:
1. Add the [tex]\(x^3\)[/tex] terms:
- From the first polynomial: [tex]\( 4x^3 \)[/tex]
- From the second polynomial: [tex]\( 3x^3 \)[/tex]
- Sum: [tex]\( (4 + 3)x^3 = 7x^3 \)[/tex]
2. Add the [tex]\(x^2\)[/tex] terms:
- From the first polynomial: [tex]\( 6x^2 \)[/tex]
- From the second polynomial: [tex]\( 3x^2 \)[/tex]
- Sum: [tex]\( (6 + 3)x^2 = 9x^2 \)[/tex]
3. Add the [tex]\(x\)[/tex] terms:
- From the first polynomial: [tex]\( 2x \)[/tex]
- From the second polynomial: [tex]\(-5x\)[/tex]
- Sum: [tex]\( (2 - 5)x = -3x \)[/tex]
4. Add the constant terms:
- From the first polynomial: [tex]\(-3\)[/tex]
- From the second polynomial: [tex]\(-5\)[/tex]
- Sum: [tex]\((-3 - 5) = -8\)[/tex]
Putting it all together, the sum of the two polynomials is:
[tex]\[ 7x^3 + 9x^2 - 3x - 8 \][/tex]
This corresponds to option 3: [tex]\(7x^3 + 9x^2 - 3x - 8\)[/tex].
We have the following polynomials:
1. [tex]\( 4x^3 + 6x^2 + 2x - 3 \)[/tex]
2. [tex]\( 3x^3 + 3x^2 - 5x - 5 \)[/tex]
Now let's add them:
1. Add the [tex]\(x^3\)[/tex] terms:
- From the first polynomial: [tex]\( 4x^3 \)[/tex]
- From the second polynomial: [tex]\( 3x^3 \)[/tex]
- Sum: [tex]\( (4 + 3)x^3 = 7x^3 \)[/tex]
2. Add the [tex]\(x^2\)[/tex] terms:
- From the first polynomial: [tex]\( 6x^2 \)[/tex]
- From the second polynomial: [tex]\( 3x^2 \)[/tex]
- Sum: [tex]\( (6 + 3)x^2 = 9x^2 \)[/tex]
3. Add the [tex]\(x\)[/tex] terms:
- From the first polynomial: [tex]\( 2x \)[/tex]
- From the second polynomial: [tex]\(-5x\)[/tex]
- Sum: [tex]\( (2 - 5)x = -3x \)[/tex]
4. Add the constant terms:
- From the first polynomial: [tex]\(-3\)[/tex]
- From the second polynomial: [tex]\(-5\)[/tex]
- Sum: [tex]\((-3 - 5) = -8\)[/tex]
Putting it all together, the sum of the two polynomials is:
[tex]\[ 7x^3 + 9x^2 - 3x - 8 \][/tex]
This corresponds to option 3: [tex]\(7x^3 + 9x^2 - 3x - 8\)[/tex].
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