Question

Three students were given the expression shown and were asked to take a

common factor out of two of the terms.

Use the drop-down menus to complete the statements about whether each

student's answer is an equivalent expression. Then choose an expression

that is equivalent



4 - 9x + 21

Answer 1

Chang's expression is incorrect because he did not divide 21 by -3 correctly.

Benjamin's expression is incorrect because he did not divide -9x by 3 correctly.

Habib's expression is incorrect because he cannot add -9x by 21.

The correct simplification of this expression is 4 - 3(3x - 7).

In Mathematics and Euclidean Geometry, factors are numbers which can be multiplied together to get another number.

In order to completely simplify the given expression, we would have to determine its common factors and then group the terms as follows;

4 - 9x + 21

The common factor of 9 and 21 is 3;

9 = 3 × 3

21 = 3 × 7

Therefore, we would factor the expression by using a common factor of 3 as follows;

4 - 3(3x - 7)

Missing information:

Three students were given the expression shown and were asked to take a common factor out of two of the terms.

Use the drop-down menus to complete the statements about whether each student's answer is an equivalent expression. Then choose an expression that is equivalent

4 - 9x + 21

Answer 2

Explanation:

The question is incomplete. Find the complete question attached.

Let us analyze each of the students expression and determine the correct one if there are any.

Chang expression after factoring: 4-3(3x+7)

In order to know whether chang's factorization is similar to the expression, we will expand and compare with the given expression as shown;

= 4-3(3x+7)

Open the parenthesis

= 4 - 3(3x)-3(7)

= 4 - 9x - 21

This shows that Chand expression is wrong.

Hence Chang expression is not an equivalent expression because when -3 is factored out from the bracket, it supposed to leave a negative sign instead of positive.

Benjamin expression after factoring: 4+3(3x+7)

In order to know whether Benjamin's factorization is similar to the expression, we will expand and compare with the given expression as shown;

= 4+3(3x+7)

Open the parenthesis

= 4 + 3(3x)+3(7)

= 4 +9x + 21

This shows that Benjamin expression is wrong.

Hence Benjamin expression is not an equivalent expression because the positive values within the expression is supposed to be negative sign instead

Habib expression after factoring: 4+12x

The equation is obviously wrong and not an equivalent expression because the constant value 21 does not have a variable x and cannot be added to -9x according to what Habib did.

Given the expression

4 - 9x + 21

The correct simplification of the expression is as shown;

4 - 3(3x - 7)

Note that when -3 is factored out, the sign inside the parenthesis also changes