Problem 6
Question
Find the degree of the polynomial. $$-4 x^{3}+7 x^{2}-11$$
Step-by-Step Solution
Verified Answer
The degree of the polynomial is 3.
1Step 1: Identify the Terms in the Polynomial
A polynomial is an expression made up of variables and coefficients. This polynomial consists of three terms: \(-4x^3\), \(7x^2\), and \(-11\).
2Step 2: Determine the Degree of Each Term
The degree of each term is given by the power of the variable (x). For the first term, \(-4x^3\), the degree is 3. The second term, \(7x^2\), has degree 2. The last term, \(-11\), has degree 0, as there is no variable attached.
3Step 3: Determine the Degree of the Polynomial
The degree of the polynomial is the highest degree among all terms in the polynomial. Thus, the degree of this polynomial is 3, which is the highest of 3, 2, and 0.
Other exercises in this chapter
Problem 6
Find all numbers that must be excluded from the domain of each rational expression. $$\frac{x-3}{x^{2}+4 x-45}$$
View solution Problem 6
$$\text { Factor out the greatest common factor.}$$ $$6 x^{4}-18 x^{3}+12 x^{2}$$
View solution Problem 6
Evaluate each expression in Exercises \(1-12,\) or indicate that the root is not a real number. $$\sqrt{-25}$$
View solution Problem 7
Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-6 x+3, \text { for } x=7$$
View solution