Question

Which polynomial has a leading coefficient of 4 and a degree of 3

Answer 1

The formula just found is an example of a polynomial, which is a sum of or ... The term with the highest degree is called the leading term because it is usually written first. ... For the following polynomials, identify the degree, the leading term, and the leading coefficient. ... The highest power of x is 3, so the degree is 3.

Explanation:

Answer 2

Answer choices:

No, A) 3 - 2 + 4 - 7

Yes, B) 4 +
`x` - 4
`x^(2)` + 5
`x^(3)`

No, C) 4
`x^(4)` - 3
`x^(3)` + 2
`x^(2)`

No, D) 2
`x` +
`x^(2)` + 4
`x^(3)`

Why B is correct:

4 +
`x` - 4
`x^(2)` + 5
`x^(3)`

The degree is 3.

The leading coefficient is -4:

- 4
`x^(2)`

Explanation:

There are lots of polynomial that has a leading coefficient of 4 and a degree of 3.

First, you need to know what is a polynomial and what it has.

The word "polynomial" comes from the root words poly- (many) and -nomial (terms).

A polynomial can have constants (numbers), variables (letters), and exponents (powers), but never negative exponents or division by a variable.

Polynomials like to be written in standard form. This means they contain no like terms and the exponents are in descending order (largest to smallest).

Degree:

The degree of a term is the sum of the exponents of the variable factors.

Leading coefficient:

Leading coefficients is the number written in front of the variable that has the largest exponent.

Example numbers:

-7
`x^(0)` +
`x^(3)` +
`x^(2)`+ -4
`x^(4)`

The standard form of writing the polynomial above is:

-4
`x^(4)` +
`x^(3)` +
`x^(2)` + -7
`x^(0)`

The degree of the polynomial is 3 or the largest exponent.

The leading coefficient is -4.