Chapter 4, Problem 1VR

Complete each statement with the correct term from the column on the right. Some of the choices may be used more than once and some may not be used at all.

product

difference

factor

factorization

grouping

ascending

descending

monomial

binomial

trinomial

zero

When the terms of a polynomial are written such that the exponents increase from left to right, we say that the polynomial is written in _________order. [4.1a]

To determine

To fill: The blank provided for the statement “When the terms of a polynomial are written such that the exponent increases from left to right, we can say that the polynomial is written in _____________order.” from the given options.

Answer to Problem 1VR

Solution:

When the terms of a polynomial are written such that the exponent increases from left to right, we can say that the polynomial is written in ascending order. So, option (f) ascending is correct.

Explanation of Solution

Given information:

The given options are:

(a) Product

(b) Difference

(c) Factor

(d) Factorization

(e) Grouping

(f) Ascending

(g) Descending

(h) Monomial

(i) Binomial

(j) Trinomial

(k) Zero

When the terms of a polynomial are arranged in ascending order, this implies that each term is arranged in a way of increasing exponents.

For example, suppose the polynomial, $4ax-7ab+4x^6-7a{x}^2$

To arrange the terms in ascending exponents of x, arrange each term one after the other in a way of increasing degree of x, this gives,

$-7ab+4ax-7a{x}^2+4x^6$

Therefore, the arrangement of ascending exponents of x in the polynomial $4ax-7ab+4x^6-7a{x}^2$ is $-7ab+4ax-7a{x}^2+4x^6$.

Thus, the correct fill for the blank is “option (f) ascending”.