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Add the polynomial expressions:

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

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

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

3. Combine like terms:
[tex]\[
-4g^4 - 3g^3 + 4g^2 + 5g + 3
\][/tex]

4. Write 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 go step-by-step to add the polynomial expressions [tex]\((g^2 - 4g^4 + 5g + 9) + (-3g^3 + 3g^2 - 6)\)[/tex]:

1. Rewrite as addition of the opposite:

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

2. Group like terms:

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

3. Combine like terms:

- The [tex]\(g^4\)[/tex] term: [tex]\(-4g^4\)[/tex]
- The [tex]\(g^3\)[/tex] term: [tex]\(-3g^3\)[/tex]
- The [tex]\(g^2\)[/tex] term: [tex]\(g^2 + 3g^2 = 4g^2\)[/tex]
- The [tex]\(g\)[/tex] term: [tex]\(5g\)[/tex]
- The constant term: [tex]\(9 + (-6) = 3\)[/tex]

4. Write the resulting polynomial in standard form:

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

So the sum of the polynomial expressions is:

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

Among the given choices, the correct one is:

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

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