Consider the polynomial [tex]f(x) = 2x^5 - 3x^4 + x - 6[/tex]. Write the degree of this polynomial, its leading term, its leading coefficient, and its constant term.

The degree of the given polynomial is [tex]\square[/tex].



Answer :

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.