Answer :
To find the difference of the polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], we'll follow these steps:
1. Distribute the Negative Sign:
First, distribute the negative sign across the second polynomial, which changes the signs of each term in that polynomial.
[tex]\[
- (6x^2 - 2x - 9) = -6x^2 + 2x + 9
\][/tex]
2. Write the Expression:
Now, rewrite the entire expression with this change:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine Like Terms:
Combine the terms that have the same degree:
- Cubic terms: There's only one cubic term, which is [tex]\(5x^3\)[/tex].
- Square terms: Combine [tex]\(4x^2\)[/tex] and [tex]\(-6x^2\)[/tex]:
[tex]\[
4x^2 - 6x^2 = -2x^2
\][/tex]
- Linear terms: There’s only one linear term, which is [tex]\(2x\)[/tex].
- Constant terms: There's only one constant, which is [tex]\(9\)[/tex].
After combining, we get:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
So, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
1. Distribute the Negative Sign:
First, distribute the negative sign across the second polynomial, which changes the signs of each term in that polynomial.
[tex]\[
- (6x^2 - 2x - 9) = -6x^2 + 2x + 9
\][/tex]
2. Write the Expression:
Now, rewrite the entire expression with this change:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine Like Terms:
Combine the terms that have the same degree:
- Cubic terms: There's only one cubic term, which is [tex]\(5x^3\)[/tex].
- Square terms: Combine [tex]\(4x^2\)[/tex] and [tex]\(-6x^2\)[/tex]:
[tex]\[
4x^2 - 6x^2 = -2x^2
\][/tex]
- Linear terms: There’s only one linear term, which is [tex]\(2x\)[/tex].
- Constant terms: There's only one constant, which is [tex]\(9\)[/tex].
After combining, we get:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
So, the difference of the polynomials is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
