Problem 114 - Algebra and Trigonometry

Question

Rewrite \(4-5 x-x^{2}+6 x^{3}\) in descending powers of \(x\).

Step-by-Step Solution

Answer

The given polynomial rewritten in descending powers of \(x\) is \(6 x^{3}-x^{2}-5 x+4\).

Step 1: Identify the Polynomial

The given expression is a polynomial: \(4-5 x-x^{2}+6 x^{3}\.

Step 2: Recognize the Powers of x

The powers of \(x\) in the given polynomial are 3, 2, 1, and 0.

Step 3: Order Terms in Descending Powers of x

Now place the polynomial terms in descending order, starting with the term with the highest power of \(x\). This results in \(6 x^{3}-x^{2}-5 x+4\).