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

1. Rewrite terms that are subtracted 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:
[tex]\[
-4g^4 - 3g^3 + 4g^2 + 5g + 3
\][/tex]

4. Write the resulting polynomial in standard form.

Complete the steps to find the sum. 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 :

To add the polynomials [tex]\(\left(g^2 - 4g^4 + 5g + 9\right) + \left(-3g^3 + 3g^2 - 6\right)\)[/tex], let's follow the steps you provided:

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

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

2. Group like terms:

Let's group terms with the same degrees together:

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

3. Combine like terms:

- Combine the [tex]\(g^4\)[/tex] terms:
[tex]\[ -4g^4 \][/tex]

- Combine the [tex]\(g^3\)[/tex] terms:
[tex]\[ -3g^3 \][/tex]

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

- Combine the [tex]\(g\)[/tex] terms:
[tex]\[ 5g \][/tex]

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

4. Write the resulting polynomial in standard form:

Standard form dictates that we should write the polynomial in descending order of the degrees of [tex]\(g\)[/tex]:

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

Thus, the sum of the polynomials is:

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

From the options given, this matches the second option:

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