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 :

Let's find the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex].

1. Identify like terms:
- Both polynomials have [tex]\(x^3\)[/tex] terms, [tex]\(7x^3\)[/tex] and [tex]\(2x^3\)[/tex].
- Both polynomials have [tex]\(x^2\)[/tex] terms, [tex]\(-4x^2\)[/tex] and [tex]\(-4x^2\)[/tex].

2. Add the coefficients of like terms:
- For the [tex]\(x^3\)[/tex] terms: Add the coefficients 7 and 2.
[tex]\[
7 + 2 = 9
\][/tex]
So, the term for [tex]\(x^3\)[/tex] in the summed polynomial is [tex]\(9x^3\)[/tex].

- For the [tex]\(x^2\)[/tex] terms: Add the coefficients [tex]\(-4\)[/tex] and [tex]\(-4\)[/tex].
[tex]\[
-4 + (-4) = -8
\][/tex]
So, the term for [tex]\(x^2\)[/tex] in the summed polynomial is [tex]\(-8x^2\)[/tex].

3. Write the result as a single polynomial:
- Combine the terms:
[tex]\[
9x^3 - 8x^2
\][/tex]

Thus, the sum of the polynomials [tex]\((7x^3 - 4x^2) + (2x^3 - 4x^2)\)[/tex] is [tex]\(9x^3 - 8x^2\)[/tex].