Problem 7 - College Algebra

Question

Find the degree of the polynomial. $$x^{2}-4 x^{3}+9 x-12 x^{4}+63$$

Step-by-Step Solution

Answer

The degree of the given polynomial \(x^{2}-4 x^{3}+9 x-12 x^{4}+63\) is 4

Step 1: Identify the Polynomial

Given the polynomial \(x^{2}-4 x^{3}+9 x-12 x^{4}+63\)

Step 2: Spot the Degrees of Each Term

The degrees of the individual terms from left to right are: 2 (from \(x^{2}\)), 3 (from \(-4x^{3}\)), 1 (from \(9x\)), 4 (from \(-12x^{4}\)) and 0 (constant term \(63\)) respectively.

Step 3: Identify the Highest Degree

Compare all the identified degrees of each term and pick the highest. In this polynomial, the highest degree is 4, from the term \(-12x^{4}\).