Chapter A.2, Problem 2E

Solution

To write the polynomial in standard form and its degree $x^2-2x-2x^3+1$ .

  $\text{Degree: 3}$

  $\text{standard form : }-2x^3+x^2-2x+1$

Given:

The polynomial function , $x^2-2x-2x^3+1$

Concept Used:

• The degree of a polynomial is the highest exponent that appears in the polynomial.
• The leading term is the first term of the polynomial after arranging the variables in descending order of exponents.
• The leading coefficient is the number with the leading term along with the sign.
• The constant term is the term which does not contain any variable in it.

Calculation:

To find the degree of the given polynomial function, we check the highest exponent appeared in the polynomial. Here in the given polynomial we can see that highest exponent on the variable x is 3.

So the degree of the polynomial is 3.

In order to write the polynomial in standard form first write the degree of each term and then write the term with higher exponents to lowest exponents and then the constant term as shown below:

The degree of the term $x^2=2$

The degree of the term $2x=1$

The degree of the term $2x^3=3$

The constant term is $1$

So, the standard form of the polynomial is $-2x^3+x^2-2x+1$ .