Question

Write a trinomial with degree 4 such that the coefficient of the term containing lowest power of variable is double the coefficient of the term containing highest power of variable.​

Answer 1

Answer:

Identifying the Degree and Leading Coefficient of Polynomials

The formula just found is an example of a polynomial, which is a sum of or difference of terms, each consisting of a variable raised to a nonnegative integer power. A number multiplied by a variable raised to an exponent, such as \displaystyle 384\pi384π, is known as a coefficient. Coefficients can be positive, negative, or zero, and can be whole numbers, decimals, or fractions. Each product \displaystyle {a}_{i}{x}^{i}a

i

x

i

, such as \displaystyle 384\pi w384πw, is a term of a polynomial. If a term does not contain a variable, it is called a constant.

A polynomial containing only one term, such as \displaystyle 5{x}^{4}5x

4

, is called a monomial. A polynomial containing two terms, such as \displaystyle 2x - 92x−9, is called a binomial. A polynomial containing three terms, such as \displaystyle -3{x}^{2}+8x - 7−3x

2

+8x−7, is called a trinomial.

We can find the degree of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term because it is usually written first. The coefficient of the leading term is called the leading coefficient. When a polynomial is written so that the powers are descending, we say that it is in standard form.

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Answer 2

Answer:

The formula just found is an example of a polynomial, which is a sum of or difference of terms, each consisting of a variable raised to a nonnegative integer power. A number multiplied by a variable raised to an exponent, such as $\displaystyle 384\pi$, is known as a coefficient.

Coefficients can be positive, negative, or zero, and can be whole numbers, decimals, or fractions. Each product...

$\displaystyle {a}_{i}{x}^{i}a¡x^i$ , such as $384\pi$, is a term of a polynomial. If a term does not contain a variable, it is called a constant.

A polynomial containing only one term, such as

$\displaystyle 5{x}^{4}5x⁴$ , is called a monomial. A polynomial containing two terms, such as

$\displaystyle 2x - 92x−9$, is called a binomial. A polynomial containing three terms, such as

$\displaystyle -3{x}^{2}+8x - 7−3x²+8x−7$, is called a trinomial.

We can find the degree of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term because it is usually written first. The coefficient of the leading term is called the leading coefficient. When a polynomial is written so that the powers are descending, we say that it is in standard form.