Mathematics, 01.12.2019 16:31 kaleec

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

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Answer from: ashhuizing

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 from: Arealbot

7x⁵ + 3x⁴ - 2x³ + 2x² - 5x + 67x⁵ - 6x⁴ + 4x² - 2x + 6Further explanation

Given:

A polynomial of the 5th degree A leading coefficient of 7A 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 = 3c = -2d = 2e = -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 = -6c = 0d = -2e = 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 moreThe remainder theorem link68.32 divided by 2.8 is divisible linkDetermine whether each algebraic expression is a polynomial or not link

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

Answer from: Quest

i can you with this sweetie!

step-by-step explanation:

Can somebody explain this to me? : ( i don't get it.

Answer from: Quest

step-by-step explanation:

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