Define the terms factor and quantity. Then for the expression −3(4+x)(z−2−y), list all of the factors, and specify which are quantities.
But what is the answer.
Factor: A factor is a number or algebraic expression that divides evenly into another number or algebraic expression. In other words, it is a value or term that can be multiplied with another value or expression to produce a certain result.
Quantity: A quantity is a numerical value that represents a count or measurement of something. It can be a specific amount or value, such as a number or measurement, that can be used in calculations.
For the expression −3(4+x)(z−2−y), let's break it down and identify all the factors:
1. Constant factor: -3
2. Parentheses factors:
a) (4+x)
b) (z-2-y)
Now, let's determine which factors are quantities:
1. Constant factor: -3 is a quantity.
2. Parentheses factors:
a) (4+x) is not a quantity since it contains a variable (x).
b) (z-2-y) is not a quantity since it also contains variables (z and y).
A factor is a number or expression that divides exactly into another number or expression. In other words, it is a component that contributes to the whole.
A quantity refers to a numerical value or an amount. It can be a specific number, a variable representing a number, or an expression that can be evaluated to a number.
Now, let's analyze the provided expression: −3(4+x)(z−2−y).
To find the factors, we look for the components that are multiplied together. In this expression, there are three main factors: −3, 4+x, and z−2−y.
Let's break them down and identify which factors are quantities:
1. −3: This is a factor. It is a constant, also known as a coefficient. It does not change in value and provides the multiplication factor to the rest of the expression. It is also a quantity because it represents a specific number.
2. 4+x: This is a factor. It consists of two terms, 4 and x, added together. It is a quantity because x represents an unknown value which can be assigned a numerical value.
3. z−2−y: This is also a factor. It consists of three terms: z, 2, and y. It is a quantity because z and y represent unknown values, and they can be assigned specific numbers.
To summarize, the factors in the expression −3(4+x)(z−2−y) are −3, 4+x, and z−2−y. All three factors are quantities since they represent specific numeric values or can be evaluated to a number.