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Answer :
To understand the given expression [tex]\(5x^3 + 25x^2 + 3x + 15\)[/tex], let's break it down by looking at its components:
1. Identify the expression: The expression is a polynomial in terms of [tex]\(x\)[/tex] with four terms: [tex]\(5x^3\)[/tex], [tex]\(25x^2\)[/tex], [tex]\(3x\)[/tex], and [tex]\(15\)[/tex].
2. Understand each term:
- [tex]\(5x^3\)[/tex]: This is the cubic term where the coefficient is 5.
- [tex]\(25x^2\)[/tex]: This is the quadratic term with a coefficient of 25.
- [tex]\(3x\)[/tex]: This is the linear term with a coefficient of 3.
- [tex]\(15\)[/tex]: This is the constant term with a value of 15.
3. Coefficients summary: From the polynomial, we have:
- The coefficient of [tex]\(x^3\)[/tex] is 5.
- The coefficient of [tex]\(x^2\)[/tex] is 25.
- The coefficient of [tex]\(x\)[/tex] is 3.
- The constant term is 15.
The coefficients for the polynomial [tex]\(5x^3 + 25x^2 + 3x + 15\)[/tex] can be represented as a set of numbers: (5, 25, 3, 15).
These coefficients provide a concise representation of the polynomial's structure, allowing you to understand its composition quickly. This breakdown could help if you needed to perform further operations like evaluating the polynomial at a specific [tex]\(x\)[/tex] value, differentiating it, or integrating it.
1. Identify the expression: The expression is a polynomial in terms of [tex]\(x\)[/tex] with four terms: [tex]\(5x^3\)[/tex], [tex]\(25x^2\)[/tex], [tex]\(3x\)[/tex], and [tex]\(15\)[/tex].
2. Understand each term:
- [tex]\(5x^3\)[/tex]: This is the cubic term where the coefficient is 5.
- [tex]\(25x^2\)[/tex]: This is the quadratic term with a coefficient of 25.
- [tex]\(3x\)[/tex]: This is the linear term with a coefficient of 3.
- [tex]\(15\)[/tex]: This is the constant term with a value of 15.
3. Coefficients summary: From the polynomial, we have:
- The coefficient of [tex]\(x^3\)[/tex] is 5.
- The coefficient of [tex]\(x^2\)[/tex] is 25.
- The coefficient of [tex]\(x\)[/tex] is 3.
- The constant term is 15.
The coefficients for the polynomial [tex]\(5x^3 + 25x^2 + 3x + 15\)[/tex] can be represented as a set of numbers: (5, 25, 3, 15).
These coefficients provide a concise representation of the polynomial's structure, allowing you to understand its composition quickly. This breakdown could help if you needed to perform further operations like evaluating the polynomial at a specific [tex]\(x\)[/tex] value, differentiating it, or integrating it.
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