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Answer :
To determine the degree and leading coefficient of a polynomial, we need to look at the terms of the polynomial and organize them by their powers of [tex]\( x \)[/tex].
The given polynomial is:
[tex]\[ x^6 - 23x^2 - 20 - 9x^4 \][/tex]
Step 1: Rearrange the Terms
First, let's write the terms in order of decreasing powers of [tex]\( x \)[/tex]:
[tex]\[ x^6 - 9x^4 - 23x^2 - 20 \][/tex]
Step 2: Identify the Degree
The degree of a polynomial is the highest power of [tex]\( x \)[/tex] in the polynomial.
In this rearranged polynomial, the highest power of [tex]\( x \)[/tex] is [tex]\( 6 \)[/tex], which comes from the term [tex]\( x^6 \)[/tex].
So, the degree of the polynomial is [tex]\( 6 \)[/tex].
Step 3: Identify the Leading Coefficient
The leading coefficient is the coefficient of the term with the highest power of [tex]\( x \)[/tex].
In this case, the term with the highest power is [tex]\( x^6 \)[/tex], and its coefficient is [tex]\( 1 \)[/tex].
Thus, the leading coefficient is [tex]\( 1 \)[/tex].
Final Answer:
- Degree: [tex]\( 6 \)[/tex]
- Leading Coefficient: [tex]\( 1 \)[/tex]
The given polynomial is:
[tex]\[ x^6 - 23x^2 - 20 - 9x^4 \][/tex]
Step 1: Rearrange the Terms
First, let's write the terms in order of decreasing powers of [tex]\( x \)[/tex]:
[tex]\[ x^6 - 9x^4 - 23x^2 - 20 \][/tex]
Step 2: Identify the Degree
The degree of a polynomial is the highest power of [tex]\( x \)[/tex] in the polynomial.
In this rearranged polynomial, the highest power of [tex]\( x \)[/tex] is [tex]\( 6 \)[/tex], which comes from the term [tex]\( x^6 \)[/tex].
So, the degree of the polynomial is [tex]\( 6 \)[/tex].
Step 3: Identify the Leading Coefficient
The leading coefficient is the coefficient of the term with the highest power of [tex]\( x \)[/tex].
In this case, the term with the highest power is [tex]\( x^6 \)[/tex], and its coefficient is [tex]\( 1 \)[/tex].
Thus, the leading coefficient is [tex]\( 1 \)[/tex].
Final Answer:
- Degree: [tex]\( 6 \)[/tex]
- Leading Coefficient: [tex]\( 1 \)[/tex]
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