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Which statements are true about the polynomial 28vw 49v 35w? check all that apply. the coefficients have no common factors other than 1. there are no common variables among all three terms. the gcf of the polynomial is 7v. each term written as the product, where one factor is the gcf, is 7(28vw) 7(49v) 35(w). the resulting expression when factoring out the gcf is 7(4vw 7v 5w).

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The statements that are true about the considered polynomial are:

  • Option 2: There are no common variables among all three terms
  • Option 5: The resulting expression when factoring out the gcf is 7(4vw+7v+5w)

How to find Greatest common factor?

Greatest common factor, as the name implies, is greatest among all common factors among the quantities given.

We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).

The considered polynomial is: 28vw + 49v + 35w

Checking all the options:

  • Option 1: The coefficients have no common factors other than 1

False.

Coefficients are numbers in multiplication with variables in each term.

The coefficients of the considered polynomial are 28, 49, 35

They are all multiple of 7 and 1, so the common factor is 7 too, along with 1.

  • Option 2: There are no common variables among all three terms

Yes its true.

It is because none of the variables v, or w are in all the three terms.

  • Option 3: The gcf of the polynomial is 7v.

False.

  1. First term = 28vw =  [tex]7\times 4 \times v \times w[/tex]
  2. Second term = 49v =  [tex]7\times 7 \times v[/tex]
  3. Third term = 35w =  [tex]7 \times 5 \times w[/tex]

Thus, the greatest factor that is common in all three terms is 7 and not 7v.

  • Option 4: Each term written as the product, where one factor is the gcf, is 7(28vw) 7(49v) 35(w)

False.

Because, each term written as product of gcf gives:

  1. First term = 28vw =  [tex]7\times 4vw[/tex]
  2. Second term = 49v =  [tex]7\times 7v[/tex]
  3. Third term = 35w =  [tex]7 \times 5w[/tex]

  • Option 5: The resulting expression when factoring out the gcf is 7(4vw+7v+5w)

True.

It is because:

[tex]7(4vw+7v+5w) = 28vw + 49v + 35w[/tex] = the considered polynomial, and that 7 is the gcf.

Thus, the statements that are true about the considered polynomial are:

  • Option 2: There are no common variables among all three terms
  • Option 5: The resulting expression when factoring out the gcf is 7(4vw+7v+5w)

Learn more about greatest common factor here:

https://brainly.com/question/207329

Answer:

The coefficients have no common factors other than 1.

There are no common variables among all three terms. <----

The GCF of the polynomial is 7v.

Each term written as the product, where one factor is the GCF, is 7(28vw) + 7(49v) + 35(w).

The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).

^^^^

Step-by-step explanation:

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