Answer :
To analyze the polynomial [tex]\( g(x) = 103x^2 + 3268 \)[/tex], let's determine its key features: the leading term, the leading coefficient, the degree, and its classification.
1. Leading Term:
- The leading term in a polynomial is the term with the highest power of [tex]\( x \)[/tex].
- For [tex]\( g(x) = 103x^2 + 3268 \)[/tex], the term with the highest power of [tex]\( x \)[/tex] is [tex]\( 103x^2 \)[/tex].
- So, the leading term is [tex]\( 103x^2 \)[/tex].
2. Leading Coefficient:
- The leading coefficient is the coefficient of the leading term.
- Since the leading term is [tex]\( 103x^2 \)[/tex], the leading coefficient is 103.
3. Degree of the Polynomial:
- The degree of a polynomial is the highest power of [tex]\( x \)[/tex] present in the polynomial.
- Here, the highest power is 2 (from [tex]\( 103x^2 \)[/tex]).
- Therefore, the degree of the polynomial is 2.
4. Classification:
- Polynomials can be classified based on their degree:
- Constant: degree 0
- Linear: degree 1
- Quadratic: degree 2
- Cubic: degree 3
- Quartic: degree 4
- Since the degree of the polynomial [tex]\( g(x) = 103x^2 + 3268 \)[/tex] is 2, it is classified as a quadratic polynomial.
In summary:
- The leading term is [tex]\( 103x^2 \)[/tex].
- The leading coefficient is 103.
- The degree is 2.
- The polynomial is classified as quadratic.
1. Leading Term:
- The leading term in a polynomial is the term with the highest power of [tex]\( x \)[/tex].
- For [tex]\( g(x) = 103x^2 + 3268 \)[/tex], the term with the highest power of [tex]\( x \)[/tex] is [tex]\( 103x^2 \)[/tex].
- So, the leading term is [tex]\( 103x^2 \)[/tex].
2. Leading Coefficient:
- The leading coefficient is the coefficient of the leading term.
- Since the leading term is [tex]\( 103x^2 \)[/tex], the leading coefficient is 103.
3. Degree of the Polynomial:
- The degree of a polynomial is the highest power of [tex]\( x \)[/tex] present in the polynomial.
- Here, the highest power is 2 (from [tex]\( 103x^2 \)[/tex]).
- Therefore, the degree of the polynomial is 2.
4. Classification:
- Polynomials can be classified based on their degree:
- Constant: degree 0
- Linear: degree 1
- Quadratic: degree 2
- Cubic: degree 3
- Quartic: degree 4
- Since the degree of the polynomial [tex]\( g(x) = 103x^2 + 3268 \)[/tex] is 2, it is classified as a quadratic polynomial.
In summary:
- The leading term is [tex]\( 103x^2 \)[/tex].
- The leading coefficient is 103.
- The degree is 2.
- The polynomial is classified as quadratic.
