how to arrange the terms of a polynomial so that the powers of x are in decending orders
a*x^n+b*x^(n-1)+c*x^(n-2)+d*x(n-3)+e*x^(n-4)...
a*x^n+b*x^(n-1)+c*x^(n-2)+d*x^(n-3)+e*x^(n-4)... +some costant
To arrange the terms of a polynomial so that the powers of x are in descending order, you need to follow these steps:
1. Start with the given polynomial in its original form.
2. Identify the highest power of x in the polynomial. This will be the term with the highest exponent.
3. Move this highest power term to the leftmost side of the polynomial.
4. Repeat steps 2 and 3 for the remaining terms in the polynomial, arranging them in descending order of their powers of x.
Let's look at an example to illustrate this process:
Example:
Given polynomial: 3x^2 + 2x^3 - 5x + 7x^4
Step 1: Start with the given polynomial.
3x^2 + 2x^3 - 5x + 7x^4
Step 2: Identify the highest power of x, which is x^4 (4th degree).
3x^2 + 2x^3 - 5x + 7x^4
Step 3: Move the highest power term to the leftmost side.
7x^4 + 3x^2 + 2x^3 - 5x
Step 4: Repeat steps 2 and 3 for the remaining terms with descending powers of x.
7x^4 + 2x^3 + 3x^2 - 5x
Now, the terms of the polynomial are arranged in descending order of their powers of x, with the highest power term (7x^4) on the leftmost side.