Question

rewrite the following polynomial in standard form.
$-dfrac{1}{9} + 10x - 2x^3 + x^5 - x^4$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written in descending order of the exponents of the variable. So we need to arrange the terms of the polynomial \( -\frac{1}{9}+10x - 2x^{3}+x^{5}-x^{4} \) from the highest exponent to the lowest exponent.

Step2: Identify the exponents of each term

• The term \( x^{5} \) has an exponent of 5.
• The term \( -x^{4} \) has an exponent of 4.
• The term \( - 2x^{3} \) has an exponent of 3.
• The term \( 10x \) can be written as \( 10x^{1} \) which has an exponent of 1.
• The term \( -\frac{1}{9} \) can be written as \( -\frac{1}{9}x^{0} \) which has an exponent of 0.

Step3: Arrange the terms in descending order of exponents

Arranging the terms \( x^{5},-x^{4}, - 2x^{3},10x,-\frac{1}{9} \) in descending order of their exponents, we get the polynomial in standard form as \( x^{5}-x^{4}-2x^{3}+10x-\frac{1}{9} \)

Answer:

\( x^{5}-x^{4}-2x^{3}+10x-\frac{1}{9} \)