Answer :
To find the difference of the given polynomials, we'll proceed step-by-step:
We have two polynomials:
1. [tex]\(5x^3 + 4x^2\)[/tex]
2. [tex]\(6x^2 - 2x - 9\)[/tex]
We need to subtract the second polynomial from the first one:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
Now, let's distribute the negative sign to each term in the second polynomial:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Next, we'll combine like terms:
1. The [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] (no like terms to combine, it remains the same)
2. The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
3. The [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex] (no like terms to combine, it remains the same)
4. The constant term is [tex]\(9\)[/tex]
Putting it all together, the resulting polynomial is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
We have two polynomials:
1. [tex]\(5x^3 + 4x^2\)[/tex]
2. [tex]\(6x^2 - 2x - 9\)[/tex]
We need to subtract the second polynomial from the first one:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
Now, let's distribute the negative sign to each term in the second polynomial:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Next, we'll combine like terms:
1. The [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] (no like terms to combine, it remains the same)
2. The [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
3. The [tex]\(x\)[/tex] term is [tex]\(2x\)[/tex] (no like terms to combine, it remains the same)
4. The constant term is [tex]\(9\)[/tex]
Putting it all together, the resulting polynomial is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
