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Answer :
To solve the problem [tex]\( (7x^3 - 15x^2 + 6x - 2) - (4x^2 + 9x - 4) \)[/tex], we need to perform polynomial subtraction. Here's how you can do it step-by-step:
1. Identify the Polynomials:
- The first polynomial is [tex]\( 7x^3 - 15x^2 + 6x - 2 \)[/tex].
- The second polynomial is [tex]\( 4x^2 + 9x - 4 \)[/tex].
2. Subtract the Second Polynomial from the First:
- To subtract, change the sign of each term in the second polynomial and then add it to the first polynomial.
[tex]\[
\text{First Polynomial: } 7x^3 - 15x^2 + 6x - 2
\][/tex]
[tex]\[
\text{Subtract: } -(4x^2 + 9x - 4) = -4x^2 - 9x + 4
\][/tex]
3. Combine Like Terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(7x^3\)[/tex] (No [tex]\(x^3\)[/tex] term in the second polynomial to combine with).
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-15x^2 - 4x^2 = -19x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x - 9x = -3x\)[/tex].
- Combine the constant terms: [tex]\(-2 + 4 = 2\)[/tex].
4. Write the Resultant Polynomial:
- Put all the combined terms together: [tex]\(7x^3 - 19x^2 - 3x + 2\)[/tex].
Hence, the simplified expression is [tex]\(\boxed{7x^3 - 19x^2 - 3x + 2}\)[/tex].
1. Identify the Polynomials:
- The first polynomial is [tex]\( 7x^3 - 15x^2 + 6x - 2 \)[/tex].
- The second polynomial is [tex]\( 4x^2 + 9x - 4 \)[/tex].
2. Subtract the Second Polynomial from the First:
- To subtract, change the sign of each term in the second polynomial and then add it to the first polynomial.
[tex]\[
\text{First Polynomial: } 7x^3 - 15x^2 + 6x - 2
\][/tex]
[tex]\[
\text{Subtract: } -(4x^2 + 9x - 4) = -4x^2 - 9x + 4
\][/tex]
3. Combine Like Terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(7x^3\)[/tex] (No [tex]\(x^3\)[/tex] term in the second polynomial to combine with).
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-15x^2 - 4x^2 = -19x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x - 9x = -3x\)[/tex].
- Combine the constant terms: [tex]\(-2 + 4 = 2\)[/tex].
4. Write the Resultant Polynomial:
- Put all the combined terms together: [tex]\(7x^3 - 19x^2 - 3x + 2\)[/tex].
Hence, the simplified expression is [tex]\(\boxed{7x^3 - 19x^2 - 3x + 2}\)[/tex].
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