Answer:
- Constant: 11
- Greatest common factor: 1
- Number of terms in the polynomial: 5
- Coefficient of the leading term: 3
- Exponent of the leading term: 2
Explanation:
In order to solve this, we need to know the definitions of the vocabulary terms and how to identify them in a polynomial expression. Here are the definitions:
- A constant is a term that has no variable. For example, 11 is a constant. It's also a prime number, but don't let that get to its head.
- A greatest common factor (GCF) is the largest number or expression that divides evenly into all the terms of a polynomial. For example, the GCF of 3x² + 4y - 5x + y + 11 is 1, because 1 is the only number that divides evenly into all the terms. It's also the loneliest number, but don't let that make you sad.
- The number of terms in a polynomial is the number of separate parts that are added or subtracted. For example, 3x² + 4y - 5x + y + 11 has five terms: 3x², 4y, -5x, y, and 11. It's also the number of fingers on one hand, but don't let that limit your counting.
- The coefficient of the leading term is the numerical factor of the term with the highest degree (the highest exponent of the variable). For example, in 3x² + 4y - 5x + y + 11, the leading term is 3x² and its coefficient is 3. It's also the number of sides on a triangle, but don't let that make you obtuse.
- The exponent of the leading term is the power of the variable in the term with the highest degree. For example, in 3x² + 4y - 5x + y + 11, the leading term is 3x² and its exponent is 2.
To match the vocabulary terms with their “parts” of the given expression, you need to drag and drop the correct numbers from the options. Here are the matches:
- Constant: 11
- Greatest common factor: 1
- Number of terms in the polynomial: 5
- Coefficient of the leading term: 3
- Exponent of the leading term: 2