Answer :
To find the sum of the two polynomials
[tex]$$
P(x) = 2x^7 + 4x^6 + 3x^2 + 2x \quad \text{and} \quad Q(x) = 3x^7 + 5x^6 + 2x^2 + 6x,
$$[/tex]
we add the coefficients of like terms.
1. For the [tex]$x^7$[/tex] terms:
[tex]$$
2x^7 + 3x^7 = (2+3)x^7 = 5x^7.
$$[/tex]
2. For the [tex]$x^6$[/tex] terms:
[tex]$$
4x^6 + 5x^6 = (4+5)x^6 = 9x^6.
$$[/tex]
3. For the [tex]$x^2$[/tex] terms:
[tex]$$
3x^2 + 2x^2 = (3+2)x^2 = 5x^2.
$$[/tex]
4. For the [tex]$x$[/tex] terms:
[tex]$$
2x + 6x = (2+6)x = 8x.
$$[/tex]
Putting these results together, the sum of the polynomials is:
[tex]$$
5x^7 + 9x^6 + 5x^2 + 8x.
$$[/tex]
This expression matches option D.
[tex]$$
P(x) = 2x^7 + 4x^6 + 3x^2 + 2x \quad \text{and} \quad Q(x) = 3x^7 + 5x^6 + 2x^2 + 6x,
$$[/tex]
we add the coefficients of like terms.
1. For the [tex]$x^7$[/tex] terms:
[tex]$$
2x^7 + 3x^7 = (2+3)x^7 = 5x^7.
$$[/tex]
2. For the [tex]$x^6$[/tex] terms:
[tex]$$
4x^6 + 5x^6 = (4+5)x^6 = 9x^6.
$$[/tex]
3. For the [tex]$x^2$[/tex] terms:
[tex]$$
3x^2 + 2x^2 = (3+2)x^2 = 5x^2.
$$[/tex]
4. For the [tex]$x$[/tex] terms:
[tex]$$
2x + 6x = (2+6)x = 8x.
$$[/tex]
Putting these results together, the sum of the polynomials is:
[tex]$$
5x^7 + 9x^6 + 5x^2 + 8x.
$$[/tex]
This expression matches option D.
