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Answer :
Sure! Let's add the two polynomials together, step by step.
We have:
[tex]\[ \left(-5x^4 + 9x^3 - 2x\right) + \left(9x^4 - 8x^3 + 7\right) \][/tex]
To add them, we'll combine the like terms, which are the terms with the same power of [tex]\( x \)[/tex].
1. Combine the [tex]\( x^4 \)[/tex] terms:
- [tex]\(-5x^4 + 9x^4\)[/tex]
- This gives us [tex]\( 4x^4 \)[/tex].
2. Combine the [tex]\( x^3 \)[/tex] terms:
- [tex]\(9x^3 - 8x^3\)[/tex]
- This gives us [tex]\( 1x^3 \)[/tex] or simply [tex]\( x^3 \)[/tex].
3. Combine the [tex]\( x \)[/tex] terms:
- There's only one [tex]\(-2x\)[/tex] term, so it stays [tex]\(-2x\)[/tex].
4. Combine the constant terms:
- The only constant term is [tex]\(+7\)[/tex].
Putting it all together, the simplified polynomial is:
[tex]\[ 4x^4 + x^3 - 2x + 7 \][/tex]
And that is the result of adding the two polynomials!
We have:
[tex]\[ \left(-5x^4 + 9x^3 - 2x\right) + \left(9x^4 - 8x^3 + 7\right) \][/tex]
To add them, we'll combine the like terms, which are the terms with the same power of [tex]\( x \)[/tex].
1. Combine the [tex]\( x^4 \)[/tex] terms:
- [tex]\(-5x^4 + 9x^4\)[/tex]
- This gives us [tex]\( 4x^4 \)[/tex].
2. Combine the [tex]\( x^3 \)[/tex] terms:
- [tex]\(9x^3 - 8x^3\)[/tex]
- This gives us [tex]\( 1x^3 \)[/tex] or simply [tex]\( x^3 \)[/tex].
3. Combine the [tex]\( x \)[/tex] terms:
- There's only one [tex]\(-2x\)[/tex] term, so it stays [tex]\(-2x\)[/tex].
4. Combine the constant terms:
- The only constant term is [tex]\(+7\)[/tex].
Putting it all together, the simplified polynomial is:
[tex]\[ 4x^4 + x^3 - 2x + 7 \][/tex]
And that is the result of adding the two polynomials!
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