Question

What is the name for this polynomial (state degree and type)
4x3 + 2x

Answer 1

The given polynomial is a cubic polynomial of the form

Step-by-step explanation:

The given polynomial is a cubic polynomial, indicated by the highest power of the variable which is in this case. The degree of a polynomial is determined by the highest power of the variable present. In this polynomial, the term with the highest power is making it a cubic polynomial.

The coefficient of the highest power term, which is 4 in this case, is crucial in identifying the type of cubic polynomial. If the leading coefficient is positive, the polynomial opens upwards, and if it is negative, it opens downwards. In this instance, the positive coefficient (4) indicates that the cubic polynomial opens upwards.

Additionally, it's important to note that there is also a linear term present in the polynomial. This term contributes to the overall structure and behavior of the polynomial. The presence of both cubic and linear terms makes this polynomial a cubic polynomial with a linear component. In summary, the given polynomial is a cubic polynomial with the expression where the highest power is 3, and the leading coefficient is 4, signifying an upward-opening cubic function with an additional linear term.

Answer 2

Name: Trinomial

Degree: 3

Type: Cubic function

Step-by-step explanation:

• Polynomials are named according to the highest power (degree) they attain;

`{ \boxed{ {ax}^{{ \boxed{n}}} + bx + c = 0 }}`

The constant n is the degree and determines the name and type of the polynomial;

• If n = 1, it's name is monomial and it's type is linear

`ax + b = 0`

• If n = 2, it's name is binomial, and it's type is a quadratic

`{ax}^(2) + bx + c = 0`

• If n = 3, it's name is trinomial, and it's type is a cubic function

`a{x}^(3) + b {x}^(2) + cx + d = 0`

• If n = 4, it's name is tetranomial and it's type is quadratic

`a {x}^(4) + {bx}^(3) + {cx}^(2) + dx + e = 0`