Question

question 9 of 10
which of the following shows the polynomial below written in descending
order?
$4x^2 - x + 8x^6 + 3 + 2x^{10}$

a. $2x^{10} + 8x^6 + 4x^2 - x + 3$

b. $3 + 2x^{10} + 8x^6 + 4x^2 - x$

c. $2x^{10} + 4x^2 - x + 3 + 8x^6$

d. $8x^6 + 4x^2 + 3 + 2x^{10} - x$

Explanation:

Step1: Recall descending order rule

Descending order of a polynomial is arranging terms by decreasing exponents of the variable (here \(x\)).

Step2: Identify exponents of each term

• For \(4x^2\), exponent is \(2\).
• For \(-x\) (or \(-x^1\)), exponent is \(1\).
• For \(8x^6\), exponent is \(6\).
• For \(3\) (or \(3x^0\)), exponent is \(0\).
• For \(2x^{10}\), exponent is \(10\).

Step3: Arrange terms by exponents (10, 6, 2, 1, 0)

• Term with \(x^{10}\): \(2x^{10}\)
• Term with \(x^6\): \(8x^6\)
• Term with \(x^2\): \(4x^2\)
• Term with \(x^1\): \(-x\)
• Term with \(x^0\): \(3\)

So the polynomial in descending order is \(2x^{10}+8x^6 + 4x^2 - x + 3\).

Answer:

A. \(2x^{10}+8x^6 + 4x^2 - x + 3\)