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]

Question

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Answer 1

Textbook Question

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]

Expert Solution & Answer

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+4x6−7ax2

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−7ax2+4x6

Therefore, the arrangement of ascending exponents of x in the polynomial 4ax−7ab+4x6−7ax2 is −7ab+4ax−7ax2+4x6.

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

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Students have asked these similar questions

ے ملزمة احمد Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to- one iff (f(x1),f(x2),...,f(x) } linearly independent. (b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a hyperplane of X. مبر خد احمد Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is convex set or not, affine set or not. Write with prove an application of Hahn-Banach theorem. Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)

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Q/(a)Let X be a finite dimension vector space over a field F and S₁,S2CX such that S₁SS2. Show that whether (1) if S, is a base for X then base for X or not (2) if S2 is a base for X then S, is a base for X or not (b) Show that every subspace of vector space is convex and affine set but the conevrse need not to be true. allet M be a non-empty subset of a vector space X over a field F and x,EX. Show that M is a hyperspace iff xo+ M is a hyperplane and xo€ xo+M. bState Hahn-Banach theorem and write with prove an application about it. Show that every singleten subset and finite subset of a normed space is closed. Oxfallet f he a function from a normad roace YI Show tha ir continuour aty.GYiff

Answer 2

Textbook Question

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]

Expert Solution & Answer

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+4x6−7ax2

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−7ax2+4x6

Therefore, the arrangement of ascending exponents of x in the polynomial 4ax−7ab+4x6−7ax2 is −7ab+4ax−7ax2+4x6.

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

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

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]

Expert Solution & Answer

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+4x6−7ax2

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−7ax2+4x6

Therefore, the arrangement of ascending exponents of x in the polynomial 4ax−7ab+4x6−7ax2 is −7ab+4ax−7ax2+4x6.

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

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

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]

Expert Solution & Answer

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+4x6−7ax2

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−7ax2+4x6

Therefore, the arrangement of ascending exponents of x in the polynomial 4ax−7ab+4x6−7ax2 is −7ab+4ax−7ax2+4x6.

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

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

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+4x6−7ax2

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−7ax2+4x6

Therefore, the arrangement of ascending exponents of x in the polynomial 4ax−7ab+4x6−7ax2 is −7ab+4ax−7ax2+4x6.

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

Answer 8

Expert Solution & Answer

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+4x6−7ax2

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−7ax2+4x6

Therefore, the arrangement of ascending exponents of x in the polynomial 4ax−7ab+4x6−7ax2 is −7ab+4ax−7ax2+4x6.

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

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

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 12

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.