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Answer :
Sure, let's go through the process step-by-step.
1. Identify the given polynomial expressions:
- The first expression is [tex]\(6x - 1 + 5x^3 - 4x^4\)[/tex].
- The second expression is [tex]\(3 - 4x - 4x^4 + 7x^3\)[/tex].
2. Combine like terms:
To add these two polynomials, we'll group and add the coefficients of like terms (i.e., terms with the same power of [tex]\(x\)[/tex]).
3. Add the constant terms:
[tex]\[
-1 + 3 = 2
\][/tex]
4. Add the [tex]\(x\)[/tex] terms:
[tex]\[
6x - 4x = 2x
\][/tex]
5. Add the [tex]\(x^3\)[/tex] terms:
[tex]\[
5x^3 + 7x^3 = 12x^3
\][/tex]
6. Add the [tex]\(x^4\)[/tex] terms:
[tex]\[
-4x^4 - 4x^4 = -8x^4
\][/tex]
7. Combine all the terms:
Putting it all together, the combined expression is:
[tex]\[
-8x^4 + 12x^3 + 2x + 2
\][/tex]
Therefore, the correct answer is option C: [tex]\(-8x^4 + 12x^3 + 2x + 2\)[/tex].
1. Identify the given polynomial expressions:
- The first expression is [tex]\(6x - 1 + 5x^3 - 4x^4\)[/tex].
- The second expression is [tex]\(3 - 4x - 4x^4 + 7x^3\)[/tex].
2. Combine like terms:
To add these two polynomials, we'll group and add the coefficients of like terms (i.e., terms with the same power of [tex]\(x\)[/tex]).
3. Add the constant terms:
[tex]\[
-1 + 3 = 2
\][/tex]
4. Add the [tex]\(x\)[/tex] terms:
[tex]\[
6x - 4x = 2x
\][/tex]
5. Add the [tex]\(x^3\)[/tex] terms:
[tex]\[
5x^3 + 7x^3 = 12x^3
\][/tex]
6. Add the [tex]\(x^4\)[/tex] terms:
[tex]\[
-4x^4 - 4x^4 = -8x^4
\][/tex]
7. Combine all the terms:
Putting it all together, the combined expression is:
[tex]\[
-8x^4 + 12x^3 + 2x + 2
\][/tex]
Therefore, the correct answer is option C: [tex]\(-8x^4 + 12x^3 + 2x + 2\)[/tex].
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