The answer is:
The polynomial will be:
[tex]7x^{5} + 8x^{4}+9x^{3}+5x^{2} +3x+6[/tex]
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:
[tex]7x^{5} + 8x^{4}+9x^{3}+5x^{2} +3x+6[/tex]
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!
Given:
Problem-solving:
Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.
[tex]\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }[/tex]
Now we make the first polynomial, for example:
Thus, the result is [tex]\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}[/tex]
Then we make the second polynomial as an alternative. For example:
Thus, the polynomial is [tex]\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}[/tex]
Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.
Notes:
Let us rephrase the following definitions.
For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]
A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:
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
