Chapter 8.1, Problem 28PPE

To determine

The polynomial $c+8c^3-3c^7$ in standard form and name polynomial based on degree and number of terms.

Answer to Problem 28PPE

The standard form of polynomial is $-3c^7+8c^3+c$ .

The polymial is Septic polynomial.

And according to number of terms polynomial is trinomial.

Explanation of Solution

Given information:

The polynomial $c+8c^3-3c^7$

Concept and Formula Used:

The standard form of a polynomial is a form in which terms are written in decreasing order of degree of variable i.e. $a_1{x}^n+a_2{x}^{n-1}+a_3{x}^{n-2}+\mathrm{..................}+a_n{x}^0$

Degree is the highest power of variable in a polynomial.

Based on degree polynomial are classified into : 1 degree Linear, 2 degree Quadratic and 3 degree Cubic

Based on number of terms polynomial are classified as Monimal containing one term, Binomial with two terms and Trinomial polynomial with three terms.

Calculation:

The givenpolynomial is $c+8c^3-3c^7$

The standard form of polynomial is $a_1{x}^n+a_2{x}^{n-1}+a_3{x}^{n-2}+\mathrm{..................}+a_n{x}^0$

The standard form of polynomial

  $c+8c^3-3c^7=-3c^7+8c^3+c$

The degree of polynomial is 2 therefore it is Quadratic polynomial.

Number of terms are 3 therefore polynomial is trinomial.

Conclusion:

The standard form of polynomial is $-3c^7+8c^3+c$ .

The polymial is Septic polynomial.

And according to number of terms polynomial is trinomial.