Question
standard form of -30x^5 - 4x^8 + 2x
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Answer
what is the leading coefficient
Answered by
GPT-4o mini
To write the polynomial \(-30x^5 - 4x^8 + 2x\) in standard form, we need to arrange the terms in descending order of their powers of \(x\).
The standard form of a polynomial is usually written as:
\[ ax^n + bx^{n-1} + cx^{n-2} + \ldots + k \]
where \(a, b, c, \ldots\) are coefficients, and \(n\) is the degree of the polynomial.
For the given polynomial:
- The term with the highest power is \(-4x^8\).
- The next term is \(-30x^5\).
- Then, we have \(2x\).
Arranging these in descending order, we get:
\[-4x^8 - 30x^5 + 2x\]
So, the polynomial in standard form is:
\[-4x^8 - 30x^5 + 2x\]
The standard form of a polynomial is usually written as:
\[ ax^n + bx^{n-1} + cx^{n-2} + \ldots + k \]
where \(a, b, c, \ldots\) are coefficients, and \(n\) is the degree of the polynomial.
For the given polynomial:
- The term with the highest power is \(-4x^8\).
- The next term is \(-30x^5\).
- Then, we have \(2x\).
Arranging these in descending order, we get:
\[-4x^8 - 30x^5 + 2x\]
So, the polynomial in standard form is:
\[-4x^8 - 30x^5 + 2x\]
Answered by
GPT-4o mini
The leading coefficient of a polynomial is the coefficient of the term with the highest degree (highest power of \(x\)).
In the polynomial \(-4x^8 - 30x^5 + 2x\), the term with the highest degree is \(-4x^8\).
Thus, the leading coefficient is \(-4\).
In the polynomial \(-4x^8 - 30x^5 + 2x\), the term with the highest degree is \(-4x^8\).
Thus, the leading coefficient is \(-4\).
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