Answered

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

2. Group like terms.

3. Combine like terms.

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 given polynomials [tex]\( \left(g^2 - 4g^4 + 5g + 9\right) \)[/tex] and [tex]\( \left(-3g^3 + 3g^2 - 6\right) \)[/tex], we follow these steps:

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

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

We can rewrite the expression to clearly show each term:
[tex]\[ g^2 + (-4g^4) + 5g + 9 + (-3g^3) + 3g^2 + (-6) \][/tex]

### Step 2: Group like terms

Group the terms according to their powers of [tex]\( g \)[/tex]:
[tex]\[ (-4g^4) + (-3g^3) + (g^2 + 3g^2) + 5g + (9 - 6) \][/tex]

### Step 3: Combine like terms

Combine the coefficients of like terms:
[tex]\[ -4g^4 - 3g^3 + (1g^2 + 3g^2) + 5g + (9 - 6) \][/tex]

Simplifying the coefficients, we get:
[tex]\[ -4g^4 - 3g^3 + 4g^2 + 5g + 3 \][/tex]

### Step 4: Write the resulting polynomial in standard form

Combine all the terms to write the polynomial in standard form:
[tex]\[ -4g^4 - 3g^3 + 4g^2 + 5g + 3 \][/tex]

Therefore, the sum of the given polynomials is:
[tex]\[ \boxed{-4g^4 - 3g^3 + 4g^2 + 5g + 3} \][/tex]