Answer :
We want to find the difference between the two polynomials:
[tex]$$ (5x^3 + 4x^2) - (6x^2 - 2x - 9). $$[/tex]
Step 1. Distribute the Negative Sign
Distribute the minus sign through the second polynomial:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9.
\][/tex]
Step 2. Combine Like Terms
Now, group and combine the like terms:
- The cubic term: [tex]\(\;5x^3\)[/tex].
- The quadratic terms: [tex]\(\;4x^2 - 6x^2 = -2x^2\)[/tex].
- The linear term: [tex]\(\;2x\)[/tex].
- The constant term: [tex]\(\;9\)[/tex].
Thus, the expression simplifies to:
[tex]\[
5x^3 - 2x^2 + 2x + 9.
\][/tex]
Final Answer
The difference of the polynomials is:
[tex]$$ \boxed{5x^3 - 2x^2 + 2x + 9}. $$[/tex]
[tex]$$ (5x^3 + 4x^2) - (6x^2 - 2x - 9). $$[/tex]
Step 1. Distribute the Negative Sign
Distribute the minus sign through the second polynomial:
[tex]\[
(5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9.
\][/tex]
Step 2. Combine Like Terms
Now, group and combine the like terms:
- The cubic term: [tex]\(\;5x^3\)[/tex].
- The quadratic terms: [tex]\(\;4x^2 - 6x^2 = -2x^2\)[/tex].
- The linear term: [tex]\(\;2x\)[/tex].
- The constant term: [tex]\(\;9\)[/tex].
Thus, the expression simplifies to:
[tex]\[
5x^3 - 2x^2 + 2x + 9.
\][/tex]
Final Answer
The difference of the polynomials is:
[tex]$$ \boxed{5x^3 - 2x^2 + 2x + 9}. $$[/tex]
