Answer :
Final answer:
The polynomial 4x12 + 9x7 + 3x3 - x is written in descending order, meaning it is arranged with the term with the highest exponent first and proceeds to the lowest.
Explanation:
The polynomial 4x12 + 9x7 + 3x3 - x is indeed written in descending order. In mathematics, ordering polynomials means arranging the terms so that the exponents of the variable decrease as you move from left to right. The given polynomial has its terms starting with the highest power of x, which is 12, and then it goes down to 7, 3, and finally to the first power of x.
Polynomials in descending order are useful for various mathematical operations, including long division, which might be used to divide polynomials like S÷P. The example given in Equation 1.16.3 or other similar instances demonstrates how polynomials are handled in operations such as integration and differentiation. It is essential for students to understand this order so that they can perform said operations correctly.
Final answer:
The polynomial 3x³ + 9x⁷ - x + 4x¹² can be written in descending order as 4x¹² + 9x⁷ + 3x³ - x. Therefore, option D is correct.
Explanation:
In the given polynomial, 3x³ + 9x⁷ - x + 4x¹², the terms with the highest degree are arranged first in descending order.
So the correct arrangement is 4x¹² + 9x⁷ + 3x³ - x.
Therefore, option D. 4x¹² + 9x⁷ + 3x³ - x shows the polynomial in descending order.
