Question

question 4 of 10
which of the following shows the polynomial below written in descending order?
$5x^3 - x + 9x^7 + 4 + 3x^{11}$

a. $3x^{11} + 9x^7 + 5x^3 - x + 4$

b. $4 + 3x^{11} + 9x^7 + 5x^3 - x$

c. $9x^7 + 5x^3 + 4 + 3x^{11} - x$

d. $3x^{11} + 9x^7 - x + 4 + 5x^3$

Explanation:

Step1: Recall descending order rule

Descending order of a polynomial is arranging terms by decreasing exponents of the variable.

Step2: Identify exponents of each term

• For \(3x^{11}\), exponent is \(11\)
• For \(9x^{7}\), exponent is \(7\)
• For \(5x^{3}\), exponent is \(3\)
• For \(-x\) (which is \(-x^{1}\)), exponent is \(1\)
• For \(4\) (which is \(4x^{0}\)), exponent is \(0\)

Step3: Arrange terms in descending order

Arrange the terms \(5x^{3}-x + 9x^{7}+4 + 3x^{11}\) by exponents from highest to lowest: \(3x^{11}\) (exponent 11), \(9x^{7}\) (exponent 7), \(5x^{3}\) (exponent 3), \(-x\) (exponent 1), \(4\) (exponent 0). So the polynomial in descending order is \(3x^{11}+9x^{7}+5x^{3}-x + 4\).

Answer:

A. \(3x^{11}+9x^{7}+5x^{3}-x + 4\)