Answered

IDNLearn.com: Your destination for reliable and timely answers to any question. Whether it's a simple query or a complex problem, our community has the answers you need.

What type of polynomial is [tex]P(x) = 4x - 2x^2 + 3[/tex]?

A. Quartic
B. Quintic
C. Cubic
D. Quadratic

Sagot :

GinnyAnsweridn
To determine the type of polynomial given by \( P(x) = 4x - 2x^2 + 3 \), we need to follow these steps:

1. Identify the Terms and Their Degrees:
- In the polynomial \( P(x) = 4x - 2x^2 + 3 \), there are three terms:
- \( 4x \): This term has a degree of 1 because the exponent of \( x \) is 1.
- \( -2x^2 \): This term has a degree of 2 because the exponent of \( x \) is 2.
- \( 3 \): This term is a constant and has a degree of 0 because there is no \( x \).

2. Determine the Degree of the Polynomial:
- The degree of a polynomial is the highest degree among its terms.
- In \( P(x) = 4x - 2x^2 + 3 \), the term with the highest degree is \( -2x^2 \), which has a degree of 2.

3. Classify the Polynomial Based on Its Degree:
- A polynomial of degree 0 is called a constant polynomial.
- A polynomial of degree 1 is called a linear polynomial.
- A polynomial of degree 2 is called a quadratic polynomial.
- A polynomial of degree 3 is called a cubic polynomial.
- A polynomial of degree 4 is called a quartic polynomial.
- A polynomial of degree 5 is called a quintic polynomial.

Since \( P(x) = 4x - 2x^2 + 3 \) has its highest degree term as \( -2x^2 \), which is of degree 2, the polynomial is classified as a quadratic polynomial.

Thus, the answer is:
D. quadratic
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.