Let's analyze the given polynomial [tex]\( f(x) = 2x^5 - 3x^4 + x - 6 \)[/tex].
### Step 1: Determine the Degree of the Polynomial
The degree of a polynomial is the highest power of [tex]\( x \)[/tex] in the polynomial.
In the given polynomial:
[tex]\[ f(x) = 2x^5 - 3x^4 + x - 6 \][/tex]
The term with the highest power of [tex]\( x \)[/tex] is [tex]\( 2x^5 \)[/tex]. The exponent of [tex]\( x \)[/tex] in this term is 5. Therefore, the degree of the polynomial is:
[tex]\[
\boxed{5}
\][/tex]
### Step 2: Identify the Leading Term
The leading term of a polynomial is the term with the highest power of [tex]\( x \)[/tex].
In [tex]\( 2x^5 - 3x^4 + x - 6 \)[/tex], the leading term is:
[tex]\[
\boxed{2x^5}
\][/tex]
### Step 3: Identify the Leading Coefficient
The leading coefficient is the coefficient of the leading term.
In the leading term [tex]\( 2x^5 \)[/tex], the coefficient is 2. So, the leading coefficient is:
[tex]\[
\boxed{2}
\][/tex]
### Step 4: Identify the Constant Term
The constant term is the term in the polynomial that does not contain any [tex]\( x \)[/tex].
In [tex]\( 2x^5 - 3x^4 + x - 6 \)[/tex], the term without [tex]\( x \)[/tex] is [tex]\( -6 \)[/tex]. So, the constant term is:
[tex]\[
\boxed{-6}
\][/tex]
To summarize:
1. The degree of the polynomial is [tex]\( 5 \)[/tex].
2. The leading term is [tex]\( 2x^5 \)[/tex].
3. The leading coefficient is [tex]\( 2 \)[/tex].
4. The constant term is [tex]\( -6 \)[/tex].
I hope this helps! If you have any more questions, feel free to ask.
