Answer :
To find the difference between the two polynomials, we'll start by understanding the problem:
We have two polynomials:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
The task is to subtract the second polynomial from the first one. Here's how you can do it step by step:
### Step 1: Write down the polynomials
The first polynomial is:
[tex]\[ 5x^3 + 4x^2 \][/tex]
The second polynomial, which we need to subtract, is:
[tex]\[ 6x^2 - 2x - 9 \][/tex]
### Step 2: Subtract the second polynomial from the first
To subtract, change the signs of each term in the second polynomial and then combine like terms with the first polynomial.
1. Change the signs:
- [tex]\( 6x^2 \)[/tex] becomes [tex]\(-6x^2\)[/tex]
- [tex]\(-2x\)[/tex] becomes [tex]\(+2x\)[/tex]
- [tex]\(-9\)[/tex] becomes [tex]\(+9\)[/tex]
2. Write the subtraction:
[tex]\( (5x^3 + 4x^2) - (6x^2 - 2x - 9) \)[/tex] becomes:
[tex]\[ 5x^3 + 4x^2 - 6x^2 + 2x + 9 \][/tex]
### Step 3: Combine like terms
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\( 4x^2 - 6x^2 = -2x^2 \)[/tex]
- There are no other [tex]\(x^3\)[/tex] or constant terms from the first polynomial to combine with, so you'll keep those as they are.
The final combined polynomial would be:
[tex]\[ 5x^3 - 2x^2 + 2x + 9 \][/tex]
So, the difference of the polynomials is:
[tex]\[ 5x^3 - 2x^2 + 2x + 9 \][/tex]
That matches option [tex]\( D \)[/tex].
We have two polynomials:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
The task is to subtract the second polynomial from the first one. Here's how you can do it step by step:
### Step 1: Write down the polynomials
The first polynomial is:
[tex]\[ 5x^3 + 4x^2 \][/tex]
The second polynomial, which we need to subtract, is:
[tex]\[ 6x^2 - 2x - 9 \][/tex]
### Step 2: Subtract the second polynomial from the first
To subtract, change the signs of each term in the second polynomial and then combine like terms with the first polynomial.
1. Change the signs:
- [tex]\( 6x^2 \)[/tex] becomes [tex]\(-6x^2\)[/tex]
- [tex]\(-2x\)[/tex] becomes [tex]\(+2x\)[/tex]
- [tex]\(-9\)[/tex] becomes [tex]\(+9\)[/tex]
2. Write the subtraction:
[tex]\( (5x^3 + 4x^2) - (6x^2 - 2x - 9) \)[/tex] becomes:
[tex]\[ 5x^3 + 4x^2 - 6x^2 + 2x + 9 \][/tex]
### Step 3: Combine like terms
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\( 4x^2 - 6x^2 = -2x^2 \)[/tex]
- There are no other [tex]\(x^3\)[/tex] or constant terms from the first polynomial to combine with, so you'll keep those as they are.
The final combined polynomial would be:
[tex]\[ 5x^3 - 2x^2 + 2x + 9 \][/tex]
So, the difference of the polynomials is:
[tex]\[ 5x^3 - 2x^2 + 2x + 9 \][/tex]
That matches option [tex]\( D \)[/tex].
