Which statement is true about the polynomial 3x2y2 − 5xy2 − 3x2y2 + 2×2 after it has been fully simplified? It has 2 terms and a degree of 2. It has 2 terms and a degree of 3. It has 4 terms and a degree of 2. It has 4 terms and a degree of 4.
The Correct Answer and Explanation is:
To find the correct answer, let’s simplify the polynomial first:
Given:
3x²y² − 5xy² − 3x²y² + 2x²
Step 1: Combine like terms
Look for like terms to simplify:
- 3x²y² and −3x²y² are like terms: 3x2y2−3x2y2=03x²y² − 3x²y² = 0 So, these cancel out.
- Now we’re left with: −5xy2+2×2−5xy² + 2x²
This is the simplified form of the polynomial.
Step 2: Count the terms
Each separate part (separated by ‘+’ or ‘−’) is a term:
- −5xy² is one term.
- +2x² is another.
So, it has 2 terms.
Step 3: Find the degree of the polynomial
The degree of a polynomial is the highest sum of exponents of variables in any single term:
- −5xy² → x¹y² → degree = 1 + 2 = 3
- 2x² → x² → degree = 2
So the highest degree is 3.
Final Answer:
✅ It has 2 terms and a degree of 3.
Explanation
A polynomial is an algebraic expression made up of terms connected by addition or subtraction, where each term is a product of a constant and variables raised to whole number powers. To analyze a polynomial, it is important to simplify it by combining like terms and then evaluate its structure.
The given polynomial is:
3x²y² − 5xy² − 3x²y² + 2x²
We begin by combining like terms. The terms 3x²y² and −3x²y² are like terms because they have the same variables with the same exponents. These cancel each other out, resulting in 0. This simplifies the expression to:
−5xy² + 2x²
Now we have two remaining terms. A term is any individual part of the expression, separated by plus or minus signs. Therefore, the polynomial has 2 terms.
Next, we determine the degree of the polynomial. The degree of each term is found by adding the exponents of all the variables in that term. For −5xy², the exponents are 1 (on x) and 2 (on y), giving a total of 3. For 2x², the exponent is 2. The degree of the entire polynomial is the highest degree among its terms, which is 3.
Thus, the fully simplified polynomial has 2 terms and a degree of 3.
✅ Correct answer: “It has 2 terms and a degree of 3.”
