Answer :
Let's analyze the given polynomials one by one to identify their degree, leading coefficient, and constant term:
### a. For the polynomial [tex]\( f(x) = x^3 - 8x^2 - x + 8 \)[/tex]:
1. Degree:
- The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex].
- In this polynomial, the highest power of [tex]\( x \)[/tex] is 3 (from the term [tex]\( x^3 \)[/tex]).
- So, the degree is 3.
2. Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- Here, the term with the highest degree is [tex]\( x^3 \)[/tex], and its coefficient is 1.
- Thus, the leading coefficient is 1.
3. Constant:
- The constant term is the term without any variable [tex]\( x \)[/tex].
- In this polynomial, the constant term is 8.
- Therefore, the constant is 8.
### c. For the polynomial [tex]\( g(x) = 13.2x^3 + 3x^4 - x - 4.4 \)[/tex]:
1. Degree:
- The degree is determined by the highest power of [tex]\( x \)[/tex].
- In this case, the highest power is 4 (from the term [tex]\( 3x^4 \)[/tex]).
- So, the degree of the polynomial is 4.
2. Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- For this polynomial, the term with the highest degree is [tex]\( 3x^4 \)[/tex], and its coefficient is 3.
- Thus, the leading coefficient is 3.
3. Constant:
- The constant term is found by looking for the term with no [tex]\( x \)[/tex] in it.
- Here, the constant is [tex]\(-4.4\)[/tex].
- Therefore, the constant is [tex]\(-4.4\)[/tex].
In conclusion:
- For [tex]\( f(x) = x^3 - 8x^2 - x + 8 \)[/tex]:
- Degree: 3
- Leading Coefficient: 1
- Constant: 8
- For [tex]\( g(x) = 13.2x^3 + 3x^4 - x - 4.4 \)[/tex]:
- Degree: 4
- Leading Coefficient: 3
- Constant: [tex]\(-4.4\)[/tex]
### a. For the polynomial [tex]\( f(x) = x^3 - 8x^2 - x + 8 \)[/tex]:
1. Degree:
- The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex].
- In this polynomial, the highest power of [tex]\( x \)[/tex] is 3 (from the term [tex]\( x^3 \)[/tex]).
- So, the degree is 3.
2. Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- Here, the term with the highest degree is [tex]\( x^3 \)[/tex], and its coefficient is 1.
- Thus, the leading coefficient is 1.
3. Constant:
- The constant term is the term without any variable [tex]\( x \)[/tex].
- In this polynomial, the constant term is 8.
- Therefore, the constant is 8.
### c. For the polynomial [tex]\( g(x) = 13.2x^3 + 3x^4 - x - 4.4 \)[/tex]:
1. Degree:
- The degree is determined by the highest power of [tex]\( x \)[/tex].
- In this case, the highest power is 4 (from the term [tex]\( 3x^4 \)[/tex]).
- So, the degree of the polynomial is 4.
2. Leading Coefficient:
- The leading coefficient is the coefficient of the term with the highest degree.
- For this polynomial, the term with the highest degree is [tex]\( 3x^4 \)[/tex], and its coefficient is 3.
- Thus, the leading coefficient is 3.
3. Constant:
- The constant term is found by looking for the term with no [tex]\( x \)[/tex] in it.
- Here, the constant is [tex]\(-4.4\)[/tex].
- Therefore, the constant is [tex]\(-4.4\)[/tex].
In conclusion:
- For [tex]\( f(x) = x^3 - 8x^2 - x + 8 \)[/tex]:
- Degree: 3
- Leading Coefficient: 1
- Constant: 8
- For [tex]\( g(x) = 13.2x^3 + 3x^4 - x - 4.4 \)[/tex]:
- Degree: 4
- Leading Coefficient: 3
- Constant: [tex]\(-4.4\)[/tex]
