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Answer :
To find the difference between the polynomials [tex]\((5x^3 + 4x^2)\)[/tex] and [tex]\((6x^2 - 2x - 9)\)[/tex], you need to subtract the second polynomial from the first. Let's go through this step-by-step:
1. Write down the polynomials:
First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
2. Align the like terms:
When subtracting polynomials, align the terms by their degrees. If a term does not exist in one of the polynomials, assume it has a coefficient of 0.
[tex]\[
\begin{aligned}
& (5x^3 + 4x^2 + 0x + 0) \\
& -(0x^3 + 6x^2 - 2x - 9)
\end{aligned}
\][/tex]
3. Subtract the coefficients:
- For [tex]\(x^3\)[/tex] terms: [tex]\(5 - 0 = 5\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(4 - 6 = -2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(0 - (-2) = 2\)[/tex]
- For the constant term: [tex]\(0 - (-9) = 9\)[/tex]
4. Write the resulting polynomial:
The final polynomial after subtraction is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
1. Write down the polynomials:
First polynomial: [tex]\(5x^3 + 4x^2\)[/tex]
Second polynomial: [tex]\(6x^2 - 2x - 9\)[/tex]
2. Align the like terms:
When subtracting polynomials, align the terms by their degrees. If a term does not exist in one of the polynomials, assume it has a coefficient of 0.
[tex]\[
\begin{aligned}
& (5x^3 + 4x^2 + 0x + 0) \\
& -(0x^3 + 6x^2 - 2x - 9)
\end{aligned}
\][/tex]
3. Subtract the coefficients:
- For [tex]\(x^3\)[/tex] terms: [tex]\(5 - 0 = 5\)[/tex]
- For [tex]\(x^2\)[/tex] terms: [tex]\(4 - 6 = -2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(0 - (-2) = 2\)[/tex]
- For the constant term: [tex]\(0 - (-9) = 9\)[/tex]
4. Write the resulting polynomial:
The final polynomial after subtraction is:
[tex]\[
5x^3 - 2x^2 + 2x + 9
\][/tex]
Therefore, the difference of the polynomials is [tex]\(5x^3 - 2x^2 + 2x + 9\)[/tex].
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