Answer :
To find the difference between the given polynomials, we need to subtract the second polynomial from the first polynomial. The polynomials we have are:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
Now, let's perform the subtraction step-by-step:
1. Setup the Expression: Write the subtraction expression:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
2. Distribute the Minus Sign: Distribute the minus sign to each term in the second polynomial:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine Like Terms:
- For the [tex]\(x^3\)[/tex] term: There's only one, [tex]\(5x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] term: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- For the [tex]\(x\)[/tex] term: The only term is [tex]\(+2x\)[/tex].
- For the constant term: The only constant is [tex]\(+9\)[/tex].
4. Write the Result: After combining the like terms, 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].
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
Now, let's perform the subtraction step-by-step:
1. Setup the Expression: Write the subtraction expression:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
\][/tex]
2. Distribute the Minus Sign: Distribute the minus sign to each term in the second polynomial:
[tex]\[
5x^3 + 4x^2 - 6x^2 + 2x + 9
\][/tex]
3. Combine Like Terms:
- For the [tex]\(x^3\)[/tex] term: There's only one, [tex]\(5x^3\)[/tex].
- For the [tex]\(x^2\)[/tex] term: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex].
- For the [tex]\(x\)[/tex] term: The only term is [tex]\(+2x\)[/tex].
- For the constant term: The only constant is [tex]\(+9\)[/tex].
4. Write the Result: After combining the like terms, 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].
