Answer :

Certainly! Let's go through the process of adding the two polynomials step by step:

You have two polynomials:

1. [tex]\(4x^4 + 9x^2 - 3\)[/tex]
2. [tex]\(-2x^4 + 5x^3 - 4\)[/tex]

The goal is to combine these polynomials by adding their like terms. Let's identify the like terms and add them:

1. Terms with [tex]\(x^4\)[/tex]:
- From the first polynomial: [tex]\(4x^4\)[/tex]
- From the second polynomial: [tex]\(-2x^4\)[/tex]

Add these coefficients:
[tex]\[
4 + (-2) = 2
\][/tex]

So, the term is [tex]\(2x^4\)[/tex].

2. Terms with [tex]\(x^3\)[/tex]:
- The first polynomial does not have a term with [tex]\(x^3\)[/tex], which means it can be considered as [tex]\(0x^3\)[/tex].
- From the second polynomial: [tex]\(5x^3\)[/tex]

Add these coefficients:
[tex]\[
0 + 5 = 5
\][/tex]

So, the term is [tex]\(5x^3\)[/tex].

3. Terms with [tex]\(x^2\)[/tex]:
- From the first polynomial: [tex]\(9x^2\)[/tex]
- The second polynomial does not have a term with [tex]\(x^2\)[/tex], which means it can be considered as [tex]\(0x^2\)[/tex].

Add these coefficients:
[tex]\[
9 + 0 = 9
\][/tex]

So, the term is [tex]\(9x^2\)[/tex].

4. Constant terms:
- From the first polynomial: [tex]\(-3\)[/tex]
- From the second polynomial: [tex]\(-4\)[/tex]

Add these coefficients:
[tex]\[
-3 + (-4) = -7
\][/tex]

Combining all like terms, we get the resulting polynomial:

[tex]\[
2x^4 + 5x^3 + 9x^2 - 7
\][/tex]

This is your final combined polynomial!

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Rewritten by : Barada