Answer :
Sure! Let's find the difference between the given polynomials step by step.
We have two polynomials:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
We need to subtract the second polynomial from the first:
[tex]\[ (5x^3 + 4x^2) - (6x^2 - 2x - 9) \][/tex]
To do this, we distribute the negative sign through the second polynomial:
[tex]\[ 5x^3 + 4x^2 - 6x^2 + 2x + 9 \][/tex]
Now, let's combine like terms:
- The cubic term is [tex]\( 5x^3 \)[/tex].
- For the quadratic terms, combine: [tex]\( 4x^2 - 6x^2 = -2x^2 \)[/tex].
- The linear term is [tex]\( 2x \)[/tex].
- The constant term is [tex]\( 9 \)[/tex].
Putting it all together, the difference of the polynomials is:
[tex]\[ 5x^3 - 2x^2 + 2x + 9 \][/tex]
So, the correct answer is:
[tex]\( 5x^3 - 2x^2 + 2x + 9 \)[/tex].
We have two polynomials:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
We need to subtract the second polynomial from the first:
[tex]\[ (5x^3 + 4x^2) - (6x^2 - 2x - 9) \][/tex]
To do this, we distribute the negative sign through the second polynomial:
[tex]\[ 5x^3 + 4x^2 - 6x^2 + 2x + 9 \][/tex]
Now, let's combine like terms:
- The cubic term is [tex]\( 5x^3 \)[/tex].
- For the quadratic terms, combine: [tex]\( 4x^2 - 6x^2 = -2x^2 \)[/tex].
- The linear term is [tex]\( 2x \)[/tex].
- The constant term is [tex]\( 9 \)[/tex].
Putting it all together, the difference of the polynomials is:
[tex]\[ 5x^3 - 2x^2 + 2x + 9 \][/tex]
So, the correct answer is:
[tex]\( 5x^3 - 2x^2 + 2x + 9 \)[/tex].
