High School

What is the sum of the polynomials?

[tex]\left(7x^3 - 4x^2\right) + \left(2x^3 - 4x^2\right)[/tex]

A. [tex]5x^3[/tex]
B. [tex]9x^3[/tex]
C. [tex]5x^3 - 8x^2[/tex]
D. [tex]9x^3 - 8x^2[/tex]

Answer :

We are given the polynomials
[tex]$$7x^3 - 4x^2$$[/tex]
and
[tex]$$2x^3 - 4x^2.$$[/tex]

To find their sum, we add the coefficients of like powers of [tex]$x$[/tex].

1. For the [tex]$x^3$[/tex] terms:
[tex]$$7x^3 + 2x^3 = (7+2)x^3 = 9x^3.$$[/tex]

2. For the [tex]$x^2$[/tex] terms:
[tex]$$-4x^2 + (-4x^2) = (-4-4)x^2 = -8x^2.$$[/tex]

Thus, the sum of the polynomials is:
[tex]$$9x^3 - 8x^2.$$[/tex]

This is the final answer.