High School

The sum of [tex]$4x^3 + 6x^2 + 2x - 3$[/tex] and [tex]$3x^3 + 3x^2 - 5x - 5$[/tex] is:

1) [tex]$7x^3 + 3x^2 - 3x - 8$[/tex]

2) [tex]$7x^3 + 3x^2 + 7x + 2$[/tex]

3) [tex]$7x^3 + 9x^2 - 3x - 8$[/tex]

4) [tex]$7x^6 + 9x^4 - 3x^2 - 8$[/tex]

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].

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