The Question(s)::
Write the polynomial
2-2x+5x^2-2x^5
in standard form.
a.) What is its degree?
b.)What is the leading coefficient?
I missed this lesson in class. It's very confusing. Could someone please explain what to do?
Much appreciated,
Rae
Rewrite the polynomial with the highest degree first, in descending degrees.
Degree means the power of x, in a polynomial, one means the highest power of x when discussing degree.
Thanks!
So, is the degree the highest exponent?
For some reason, I keep thinking it's five.
But, I might be wrong.
Hi Rae! I'd be happy to help you understand how to write a polynomial in standard form and find its degree and leading coefficient.
To write a polynomial in standard form, we arrange the terms in descending order of their degrees. The degree of a term is the exponent of the variable. In this case, our polynomial is 2-2x+5x^2-2x^5.
To put it in standard form, we start by arranging the terms in descending order of their degrees. So, let's rewrite the polynomial:
-2x^5 + 5x^2 - 2x + 2
Now the terms are in the desired order.
Now let's move on to finding the degree of the polynomial. The degree of a polynomial is the highest exponent of the variable present in any term. In this case, the highest exponent is 5. So, the degree of the polynomial is 5.
The leading coefficient is the coefficient of the term with the highest degree. In this case, the term with the highest degree is -2x^5, and its coefficient is -2. Therefore, the leading coefficient of the polynomial is -2.
So, to summarize:
a.) The degree of the polynomial is 5.
b.) The leading coefficient of the polynomial is -2.
I hope this helps! Let me know if you have any further questions.