Problem 7
Question
Find the degree of the polynomial. $$x^{2}-4 x^{3}+9 x-12 x^{4}+63$$
Step-by-Step Solution
Verified Answer
The degree of the polynomial \(x^{2}-4 x^{3}+9 x-12 x^{4}+63\) is 4.
1Step 1: Identify the terms
The given polynomial is \(x^{2}-4 x^{3}+9 x-12 x^{4}+63\). This polynomial has five terms: \(x^{2}\), \(-4 x^{3}\), \(9 x\), \(-12 x^{4}\), and \(63\).
2Step 2: Find the powers
The powers of 'x' in the five terms, respectively, are 2, 3, 1, 4, and 0 (since there is no 'x' in the term \(63\), we can consider the power of 'x' in that term to be 0).
3Step 3: Identify the highest power
Among the powers 2, 3, 1, 4, and 0, the highest is 4.
Other exercises in this chapter
Problem 7
Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{3 x-9}{x^{2}-6 x+9}$$
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$$\text { Factor out the greatest common factor.}$$ $$x(x+5)+3(x+5)$$
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Evaluate each expression in Exercises \(1-12,\) or indicate that the root is not a real number. $$\sqrt{25-16}$$
View solution Problem 8
Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-7 x+4, \text { for } x=8$$
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