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Add: [tex]\((g^2 - 4g^4 + 5g + 9) + (-3g^3 + 3g^2 - 6)\)[/tex]

1. Rewrite terms:
[tex]\[g^2 + (-4g^4) + 5g + 9 + (-3g^3) + 3g^2 + (-6)\][/tex]

2. Group like terms.

3. Combine like terms.

4. Write the resulting polynomial in standard form.

What is the sum?

A. [tex]\(-7g^4 + 4g^3 - 3g^2 + 5g - 3\)[/tex]

B. [tex]\(-4g^4 - 3g^3 + 4g^2 + 5g + 3\)[/tex]

C. [tex]\(-4g^4 + 4g^2 + 14g - 6\)[/tex]

D. [tex]\(-3g^4 + 14g - 6\)[/tex]



Answer :

GinnyAnswer
Let's add the polynomials [tex]\(\left(g^2 - 4g^4 + 5g + 9\right) + \left(-3g^3 + 3g^2 - 6\right)\)[/tex] step by step:

1. Rewrite terms that are subtracted as addition of the opposite:

[tex]\[ g^2 + \left(-4g^4\right) + 5g + 9 + \left(-3g^3\right) + 3g^2 + (-6) \][/tex]

2. Group like terms:

Combine the terms with the same degrees of [tex]\(g\)[/tex]:

- Terms with [tex]\(g^4\)[/tex]: [tex]\(-4g^4\)[/tex]
- Terms with [tex]\(g^3\)[/tex]: [tex]\(-3g^3\)[/tex]
- Terms with [tex]\(g^2\)[/tex]: [tex]\(g^2 + 3g^2\)[/tex]
- Terms with [tex]\(g\)[/tex]: [tex]\(5g\)[/tex]
- Constant terms: [tex]\(9 + (-6)\)[/tex]

3. Combine like terms:

- Combine the [tex]\(g^2\)[/tex] terms: [tex]\(g^2 + 3g^2 = 4g^2\)[/tex]
- Combine the constant terms: [tex]\(9 + (-6) = 3\)[/tex]

Now list all terms:

- [tex]\(-4g^4\)[/tex]
- [tex]\(-3g^3\)[/tex]
- [tex]\(4g^2\)[/tex]
- [tex]\(5g\)[/tex]
- [tex]\(3\)[/tex]

4. Write the resulting polynomial in standard form:

Arrange from the highest power of [tex]\(g\)[/tex] to the lowest power:

[tex]\[ -4g^4 - 3g^3 + 4g^2 + 5g + 3 \][/tex]

Therefore, the sum of the polynomials [tex]\(\left(g^2 - 4g^4 + 5g + 9\right) + \left(-3g^3 + 3g^2 - 6\right)\)[/tex] is:

[tex]\[ \boxed{-4g^4 - 3g^3 + 4g^2 + 5g + 3} \][/tex]

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