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Answer :
To find the standard form of the given polynomial expression, we'll combine like terms from the expression to simplify it. Here's the step-by-step breakdown:
1. Identify and rearrange the terms:
The given polynomial expression is:
[tex]\[
9x^2 + 5x + 27 + 2x^3 + 9x^2 + 5x + 9x^2 + 2x^3 + 27
\][/tex]
Let's rearrange the terms by their degrees:
[tex]\[
(2x^3 + 2x^3) + (9x^2 + 9x^2 + 9x^2) + (5x + 5x) + (27 + 27)
\][/tex]
2. Combine the like terms:
- Terms with [tex]\(x^3\)[/tex]: [tex]\(2 + 2 = 4\)[/tex], so the coefficient for [tex]\(x^3\)[/tex] is [tex]\(4\)[/tex].
- Terms with [tex]\(x^2\)[/tex]: [tex]\(9 + 9 + 9 = 27\)[/tex], so the coefficient for [tex]\(x^2\)[/tex] is [tex]\(27\)[/tex].
- Terms with [tex]\(x\)[/tex]: [tex]\(5 + 5 = 10\)[/tex], so the coefficient for [tex]\(x\)[/tex] is [tex]\(10\)[/tex].
- Constant terms: [tex]\(27 + 27 = 54\)[/tex].
3. Write the polynomial in standard form:
The standard form of the polynomial, which arranges terms from highest to lowest degree, is:
[tex]\[
4x^3 + 27x^2 + 10x + 54
\][/tex]
So, the simplified polynomial in standard form is [tex]\(4x^3 + 27x^2 + 10x + 54\)[/tex].
1. Identify and rearrange the terms:
The given polynomial expression is:
[tex]\[
9x^2 + 5x + 27 + 2x^3 + 9x^2 + 5x + 9x^2 + 2x^3 + 27
\][/tex]
Let's rearrange the terms by their degrees:
[tex]\[
(2x^3 + 2x^3) + (9x^2 + 9x^2 + 9x^2) + (5x + 5x) + (27 + 27)
\][/tex]
2. Combine the like terms:
- Terms with [tex]\(x^3\)[/tex]: [tex]\(2 + 2 = 4\)[/tex], so the coefficient for [tex]\(x^3\)[/tex] is [tex]\(4\)[/tex].
- Terms with [tex]\(x^2\)[/tex]: [tex]\(9 + 9 + 9 = 27\)[/tex], so the coefficient for [tex]\(x^2\)[/tex] is [tex]\(27\)[/tex].
- Terms with [tex]\(x\)[/tex]: [tex]\(5 + 5 = 10\)[/tex], so the coefficient for [tex]\(x\)[/tex] is [tex]\(10\)[/tex].
- Constant terms: [tex]\(27 + 27 = 54\)[/tex].
3. Write the polynomial in standard form:
The standard form of the polynomial, which arranges terms from highest to lowest degree, is:
[tex]\[
4x^3 + 27x^2 + 10x + 54
\][/tex]
So, the simplified polynomial in standard form is [tex]\(4x^3 + 27x^2 + 10x + 54\)[/tex].
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