Answer :
Sure! Let's find the difference between the two polynomials step by step.
We start with the expression:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
Step 1: Distribute the negative sign
We need to distribute the negative sign to each term in the second polynomial. This changes the signs of each term within the parentheses:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Step 2: Combine like terms
Now, we'll combine the terms with the same degree:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- There's no like term for [tex]\(5x^3\)[/tex], so it stays as [tex]\(5x^3\)[/tex].
- The [tex]\(2x\)[/tex] term also has no like term, so it remains [tex]\(2x\)[/tex].
- The constant term [tex]\(+9\)[/tex] remains unchanged as there's no other constant to combine.
Step 3: Write the final expression
Putting it all together, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
So, the answer is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
We start with the expression:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
Step 1: Distribute the negative sign
We need to distribute the negative sign to each term in the second polynomial. This changes the signs of each term within the parentheses:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
Step 2: Combine like terms
Now, we'll combine the terms with the same degree:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- There's no like term for [tex]\(5x^3\)[/tex], so it stays as [tex]\(5x^3\)[/tex].
- The [tex]\(2x\)[/tex] term also has no like term, so it remains [tex]\(2x\)[/tex].
- The constant term [tex]\(+9\)[/tex] remains unchanged as there's no other constant to combine.
Step 3: Write the final expression
Putting it all together, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
So, the answer is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
