for the polynomial complete the following table, -7x^4+8x^3-8x^2+3x-4. Degree of the term, Coefficient, Degree of the term, Degree of the Polynomial. Thank you.
-7x^4 + 8x^3 - 8x^2 + 3x-4
The first term in the polynomial, when it is written in decreasing order, is also the term with the biggest exponent, and is called the "leading term".
The exponent on a term tells you the "degree" of the term. For instance, the leading term in the above polynomial is a "fourth-degree term" or "a term of degree four". The second term is a "third degree" term.
The degree of the leading term tells you the degree of the whole polynomial (when written in decreasing order); the polynomial above is a "fourth-degree polynomial".
http://www.purplemath.com/modules/polydefs.htm
To complete the table, we need to determine the degree of each term, its coefficient, and the degree of the polynomial.
First, let's break down the given polynomial: -7x^4 + 8x^3 - 8x^2 + 3x - 4
Term Coefficient Degree
-7x^4 -7 4
8x^3 8 3
-8x^2 -8 2
3x 3 1
-4 -4 0
Now, let's calculate the degree of the polynomial. The degree of a polynomial is the highest power of x in any term. Here, the term with the highest degree is -7x^4, which has a degree of 4. Therefore, the degree of the polynomial is 4.
To summarize the table:
Term Coefficient Degree
-7x^4 -7 4
8x^3 8 3
-8x^2 -8 2
3x 3 1
-4 -4 0
The degree of the polynomial is 4.