Chapter 8, Problem 6CR

To determine

The polynomial $4r+3-9r^2+7r$ in standard form and name polynomial based on degree and number of terms.

Answer to Problem 6CR

The standard form of polynomial is $-9r^2+11r+3$ .

The is Quadratic polynomial.

And according to number of terms polynomial is trinomial.

Explanation of Solution

Given information:

The polynomial $4r+3-9r^2+7r$

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 $4r+3-9r^2+7r$

On simplifying

  $4r+3-9r^2+7r=11r+3-9r^2$

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

  $4r+3-9r^2+7r=-9r^2+11r+3$

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 $-9r^2+11r+3$ .

The is Quadratic polynomial.

And according to number of terms polynomial is trinomial.