Answer :
To add the two polynomials
[tex]$$
\left(4 x^5 - 70 x^4 + 6 x^3 - 4 x^2 + 6 x - 4\right) + \left(3 x^5 - 4 x^4 - 6 x^3 - 4 x^2 + 6 x - 4\right),
$$[/tex]
we combine like terms by matching the powers of [tex]$x$[/tex].
1. For the [tex]$x^5$[/tex] terms:
[tex]$$4x^5 + 3x^5 = 7x^5.$$[/tex]
2. For the [tex]$x^4$[/tex] terms:
[tex]$$-70x^4 - 4x^4 = -74x^4.$$[/tex]
3. For the [tex]$x^3$[/tex] terms:
[tex]$$6x^3 - 6x^3 = 0x^3.$$[/tex]
This term cancels out.
4. For the [tex]$x^2$[/tex] terms:
[tex]$$-4x^2 - 4x^2 = -8x^2.$$[/tex]
5. For the [tex]$x^1$[/tex] (or simply [tex]$x$[/tex]) terms:
[tex]$$6x + 6x = 12x.$$[/tex]
6. For the constant terms:
[tex]$$-4 - 4 = -8.$$[/tex]
Putting it all together, the sum of the two polynomials is
[tex]$$
7x^5 - 74x^4 - 8x^2 + 12x - 8.
$$[/tex]
This is the final simplified expression.
[tex]$$
\left(4 x^5 - 70 x^4 + 6 x^3 - 4 x^2 + 6 x - 4\right) + \left(3 x^5 - 4 x^4 - 6 x^3 - 4 x^2 + 6 x - 4\right),
$$[/tex]
we combine like terms by matching the powers of [tex]$x$[/tex].
1. For the [tex]$x^5$[/tex] terms:
[tex]$$4x^5 + 3x^5 = 7x^5.$$[/tex]
2. For the [tex]$x^4$[/tex] terms:
[tex]$$-70x^4 - 4x^4 = -74x^4.$$[/tex]
3. For the [tex]$x^3$[/tex] terms:
[tex]$$6x^3 - 6x^3 = 0x^3.$$[/tex]
This term cancels out.
4. For the [tex]$x^2$[/tex] terms:
[tex]$$-4x^2 - 4x^2 = -8x^2.$$[/tex]
5. For the [tex]$x^1$[/tex] (or simply [tex]$x$[/tex]) terms:
[tex]$$6x + 6x = 12x.$$[/tex]
6. For the constant terms:
[tex]$$-4 - 4 = -8.$$[/tex]
Putting it all together, the sum of the two polynomials is
[tex]$$
7x^5 - 74x^4 - 8x^2 + 12x - 8.
$$[/tex]
This is the final simplified expression.
