Question 8 of 10

Choose two statements that are true for this expression:

[tex]\[ 6x^3 - 8x^2 - \frac{40}{y} + 21 \][/tex]

A. There are four terms.
B. The term [tex]\(-\frac{40}{y}\)[/tex] is a ratio.
C. There are three terms.
D. The entire expression is a difference.



Answer :

To determine which statements about the given expression [tex]\( 6x^3 - 8x^2 - \frac{40}{y} + 21 \)[/tex] are true, we need to analyze its structure carefully.

1. First, identify the terms of the expression: A mathematical term is a component separated by addition or subtraction operators.
- The expression [tex]\( 6x^3 \)[/tex] is one term.
- The expression [tex]\(-8x^2 \)[/tex] is another term.
- The expression [tex]\(-\frac{40}{y} \)[/tex] is a term.
- The constant [tex]\( 21 \)[/tex] is also a term.

So, there are a total of four terms in the expression. Therefore, statement A is true.

2. Next, consider the term [tex]\(-\frac{40}{y} \)[/tex]:
- This term represents a ratio or a fraction, since it involves division where [tex]\( -40 \)[/tex] is divided by [tex]\( y \)[/tex].

Therefore, statement B is true.

3. Examine if the expression has three terms:
- As concluded earlier, the expression has four terms.

Hence, statement C is false.

4. Determine if the entire expression is a difference:
- A difference implies that the whole expression is subtracting one quantity from another. In our case, the expression involves a combination of subtraction and addition between four terms and not exclusively a single difference.

Thus, statement D is false.

Summarizing the true statements:

- A. There are four terms.
- B. The term [tex]\(-\frac{40}{y} \)[/tex] is a ratio.

These two statements are true for the given expression.