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.
