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Answer :
To find the difference of the given polynomials, we will follow these steps:
1. Identify the Polynomials:
The polynomials given are:
- First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
2. Subtract the Second Polynomial from the First:
We need to subtract the second polynomial from the first polynomial. This means we will distribute the negative sign across the second polynomial and then combine like terms.
Expression:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
3. Distribute the Negative Sign:
Distribute the negative sign across the second polynomial:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]
4. Combine Like Terms:
Now, combine the terms of the polynomials:
- The terms with [tex]\(x^3\)[/tex] are: [tex]\(5x^3\)[/tex]
- The terms with [tex]\(x^2\)[/tex] are: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- The terms with [tex]\(x\)[/tex] are: [tex]\(+2x\)[/tex]
- The constant terms are: [tex]\(+9\)[/tex]
5. Write the Final Difference:
The simplified polynomial, after combining like terms, is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This is the difference of the given polynomials.
1. Identify the Polynomials:
The polynomials given are:
- First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
- Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
2. Subtract the Second Polynomial from the First:
We need to subtract the second polynomial from the first polynomial. This means we will distribute the negative sign across the second polynomial and then combine like terms.
Expression:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
3. Distribute the Negative Sign:
Distribute the negative sign across the second polynomial:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]
4. Combine Like Terms:
Now, combine the terms of the polynomials:
- The terms with [tex]\(x^3\)[/tex] are: [tex]\(5x^3\)[/tex]
- The terms with [tex]\(x^2\)[/tex] are: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- The terms with [tex]\(x\)[/tex] are: [tex]\(+2x\)[/tex]
- The constant terms are: [tex]\(+9\)[/tex]
5. Write the Final Difference:
The simplified polynomial, after combining like terms, is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
This is the difference of the given polynomials.
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