Answer :
To find the difference of the two polynomials [tex]\((5x^3 + 4x^2) - (6x^2 - 2x - 9)\)[/tex], follow these steps:
1. Distribute the negative sign:
When you have a subtraction involving parentheses, distribute the negative sign (or think of it as multiplying by [tex]\(-1\)[/tex]) across all terms in the second polynomial. This changes the subtraction into addition of negative terms:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]
2. Combine the polynomials:
Now, combine like terms from both polynomials:
- Cubic term: You only have one term with [tex]\(x^3\)[/tex], which is [tex]\(5x^3\)[/tex].
- Quadratic terms: Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- Linear term: The only [tex]\(x\)[/tex] term is [tex]\(+2x\)[/tex].
- Constant term: The only constant number is [tex]\(+9\)[/tex].
3. Write the final expression:
Putting all the terms together, the simplified 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].
1. Distribute the negative sign:
When you have a subtraction involving parentheses, distribute the negative sign (or think of it as multiplying by [tex]\(-1\)[/tex]) across all terms in the second polynomial. This changes the subtraction into addition of negative terms:
[tex]\[
(5x^3 + 4x^2) - 6x^2 + 2x + 9
\][/tex]
2. Combine the polynomials:
Now, combine like terms from both polynomials:
- Cubic term: You only have one term with [tex]\(x^3\)[/tex], which is [tex]\(5x^3\)[/tex].
- Quadratic terms: Combine the [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- Linear term: The only [tex]\(x\)[/tex] term is [tex]\(+2x\)[/tex].
- Constant term: The only constant number is [tex]\(+9\)[/tex].
3. Write the final expression:
Putting all the terms together, the simplified 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].
