Question

A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6

Answer 1

Hello!

The answer is:

The polynomial will be:

$7x^{5} + 8x^{4}+9x^{3}+5x^{2} +3x+6$

Why?

To write the asked polynomial, we must remember the following:

- The leading coefficient is the coefficient of the highest degree term.

- The degree of the polynomial is defined by its highest exponent.

- The constant terms are terms like numbers or letters that are not related to the variable.

So, we are asked to write a polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6, so, it will be:

Let "x" be the variable, so, the polynomial will be:

$7x^{5} + 8x^{4}+9x^{3}+5x^{2} +3x+6$

We can see that it has a leading coefficient of 7, is a 5th-degree polynomial and has a constant term of 6.

Have a nice day!

Answer 2

• 7x⁵ + 3x⁴ - 2x³ + 2x² - 5x + 6
• 7x⁵ - 6x⁴ + 4x² - 2x + 6

Further explanation

Given:

• A polynomial of the 5th degree
• A leading coefficient of 7
• A constant term of 6

Problem-solving:

Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.

$\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }$

Now we make the first polynomial, for example:

• b = 3
• c = -2
• d = 2
• e = -5

Thus, the result is $\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}$

Then we make the second polynomial as an alternative. For example:

• b = -6
• c = 0
• d = -2
• e = 0

Thus, the polynomial is $\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}$

Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.

Notes:

Let us rephrase the following definitions.

• A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example, $\boxed{-2} \boxed{3x^2} \boxed{4a^3b^4} \boxed{-5xy^3z^2} \boxed{\frac{3}{5}}$
• A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above $\boxed{ \ -2, 3, 4, -5, \frac{3}{5} \ }$ are the coefficients.
• A polynomial is the sum or difference of a set of monomials. For example, $\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }$
• Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial $\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }$ are $\boxed{ \ 2, - 3, and \ 4. \ }$
• The constant term is the term of polynomial that does not contain a variable.
• The leading coefficient is the coefficient of the term containing the variable raised to the highest power.

For example, consider the polynomial $\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }$

• $\boxed{ \ 2x^4, - 3x^2, - 4x, and \ - 5 \ }$ are the terms of polynomial.
• $\boxed{ \ 2, - 3, - 4 \ }$ are the coefficients.
• - 5 is the constant term.
• 2 is the leading coefficient.

A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:

• $\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }$ is a polynomial in standard form.
• $\boxed{ \ - 3x^2 + 2x^4 - 5- 4x \ }$ is the polynomial, but it is not in standard form.

Learn more

1. The remainder theorem brainly.com/question/9500387
2. 68.32 divided by 2.8 is divisible  brainly.com/question/5022643#
3. Determine whether each algebraic expression is a polynomial or not brainly.com/question/9184197#

Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer