Final answer:
Each polynomial simplifies as follows: Polynomial 1 simplifies to -126, which is a Monomial. Polynomial 2 simplifies to 7x^2 - 2089.9, which is a Binomial. Polynomial 3 simplifies to -20x^2 - 27.52, which is also a Binomial.
Step-by-step explanation:
To simplify the given polynomials and identify the number of terms in each, we will carry out the appropriate algebraic operations. Let's simplify each polynomial one by one:
Polynomial 1: (1 - 3)(61 + 2)
First, perform the multiplication:
-2 × 61 = -122
-2 × 2 = -4
Now, combine these two products:
-122 - 4 = -126
Since there is only one term left after simplification, Polynomial 1 is a Monomial.
Polynomial 2: (7x^2 + 3.1) – (2102 – 12)
Subtract the second grouping from the first:
7x^2 + 3.1 - 2102 + 12
Now, combine like terms:
7x^2 - 2089.9
This is a Binomial because it consists of two terms.
Polynomial 3: 4(5.12 – 95 + 7) + 2(–10x^2 + 180 – 13)
Multiply each term inside the parentheses by the constants outside:
4 × 5.12 = 20.48
4 × (-95) = -380
4 × 7 = 28
2 × (-10x^2) = -20x^2
2 × 180 = 360
2 × (-13) = -26
Next, combine like terms:
-20x^2 + 20.48 - 380 + 28 + 360 - 26
-20x^2 - 27.52
This simplifies down to a Binomial.
After simplifying, we can eliminate terms wherever possible. It's important to check if the resulting terms make sense by ensuring the numbers and variables match properly as well as adhering to the correct operations of addition and subtraction.