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Answer :
Sure! Let's work through the problem of finding the difference between the polynomials step by step.
We're given two polynomials:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
The problem asks us to find the difference between these two polynomials, which means we need to subtract the second polynomial from the first.
Here's how to do it:
### Step 1: Set up the Subtraction
Write down the expression for the subtraction:
[tex]\( (5x^3 + 4x^2) - (6x^2 - 2x - 9) \)[/tex]
### Step 2: Distribute the Negative Sign
When subtracting a polynomial, you must distribute the negative sign across the entire second polynomial:
[tex]\( 5x^3 + 4x^2 - 6x^2 + 2x + 9 \)[/tex]
### Step 3: Combine Like Terms
Combine like terms by adding or subtracting the coefficients of terms with the same degree:
- The [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] remains unchanged since there's no other [tex]\(x^3\)[/tex] term to combine with.
- The [tex]\(x^2\)[/tex] term: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- The [tex]\(x\)[/tex] term: [tex]\(0x + 2x = 2x\)[/tex] (there's no [tex]\(x\)[/tex] term in the first polynomial, hence it's treated as [tex]\(0x\)[/tex] initially)
- The constant term: [tex]\(+9\)[/tex] remains unchanged as there's no other constant to combine with.
### Step 4: Write the Result
After combining the terms, the resulting polynomial is:
[tex]\( 5x^3 - 2x^2 + 2x + 9 \)[/tex]
That's your final answer for the difference of the polynomials!
We're given two polynomials:
1. [tex]\( 5x^3 + 4x^2 \)[/tex]
2. [tex]\( 6x^2 - 2x - 9 \)[/tex]
The problem asks us to find the difference between these two polynomials, which means we need to subtract the second polynomial from the first.
Here's how to do it:
### Step 1: Set up the Subtraction
Write down the expression for the subtraction:
[tex]\( (5x^3 + 4x^2) - (6x^2 - 2x - 9) \)[/tex]
### Step 2: Distribute the Negative Sign
When subtracting a polynomial, you must distribute the negative sign across the entire second polynomial:
[tex]\( 5x^3 + 4x^2 - 6x^2 + 2x + 9 \)[/tex]
### Step 3: Combine Like Terms
Combine like terms by adding or subtracting the coefficients of terms with the same degree:
- The [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex] remains unchanged since there's no other [tex]\(x^3\)[/tex] term to combine with.
- The [tex]\(x^2\)[/tex] term: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- The [tex]\(x\)[/tex] term: [tex]\(0x + 2x = 2x\)[/tex] (there's no [tex]\(x\)[/tex] term in the first polynomial, hence it's treated as [tex]\(0x\)[/tex] initially)
- The constant term: [tex]\(+9\)[/tex] remains unchanged as there's no other constant to combine with.
### Step 4: Write the Result
After combining the terms, the resulting polynomial is:
[tex]\( 5x^3 - 2x^2 + 2x + 9 \)[/tex]
That's your final answer for the difference of the polynomials!
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