Sure! Let’s solve each problem by finding the
degree of each polynomial.
---
📌 What is the degree of a polynomial?
> The
degree of a polynomial is the
highest degree of any term in the polynomial.
> The
degree of a term is the
sum of the exponents of all variables in that term.
---
Let’s go one by one:
---
1) `x³ + 8 - 5x⁴y + xy²`
- Term 1: `x³` → degree = 3
- Term 2: `8` → constant → degree = 0
- Term 3: `-5x⁴y` → x⁴ and y¹ → 4 + 1 =
5
- Term 4: `xy²` → x¹ and y² → 1 + 2 = 3
✔ Highest degree = 5
---
2) `s⁵ - 2q⁷r⁴s`
- Term 1: `s⁵` → degree = 5
- Term 2: `-2q⁷r⁴s` → q⁷, r⁴, s¹ → 7 + 4 + 1 =
12
✔ Highest degree = 12
---
3) `m - 7 - m³ - m²`
- All terms are in variable `m`
- `m` → degree 1
- `-7` → 0
- `-m³` → 3
- `-m²` → 2
✔ Highest degree = 3
---
4) `-y⁶ + z³ + 6 - 4z² + 5y³`
- `-y⁶` → 6
- `z³` → 3
- `6` → 0
- `-4z²` → 2
- `5y³` → 3
✔ Highest degree = 6
---
5) `7a⁵ + b⁶ + 5 + c + a⁴b²c³`
- `7a⁵` → 5
- `b⁶` → 6
- `5` → 0
- `c` → 1
- `a⁴b²c³` → 4 + 2 + 3 =
9
✔ Highest degree = 9
---
6) `u⁶ - 8v⁵ - 9u⁷v³`
- `u⁶` → 6
- `-8v⁵` → 5
- `-9u⁷v³` → 7 + 3 =
10
✔ Highest degree = 10
---
7) `-m² - 2n + m⁵n³ - 4 - 5n²`
- `-m²` → 2
- `-2n` → 1
- `m⁵n³` → 5 + 3 =
8
- `-4` → 0
- `-5n²` → 2
✔ Highest degree = 8
---
8) `-3 + 4a`
- `-3` → 0
- `4a` → 1
✔ Highest degree = 1
---
9) `-10`
- This is a
constant → no variables → degree =
0
✔ Degree = 0
---
10) `9x²t + x⁵t⁶ + 3t³ - 7st² - s³ - 2t²`
- `9x²t` → x², t¹ → 2 + 1 = 3
- `x⁵t⁶` → 5 + 6 =
11
- `3t³` → 3
- `-7st²` → s¹, t² → 1 + 2 = 3
- `-s³` → 3
- `-2t²` → 2
✔ Highest degree = 11
---
11) `p² + 6q`
- `p²` → 2
- `6q` → 1
✔ Highest degree = 2
---
12) `n²v²w² + 2uv - 7v - u²`
- `n²v²w²` → 2 + 2 + 2 =
6
- `2uv` → 1 + 1 = 2
- `-7v` → 1
- `-u²` → 2
✔ Highest degree = 6
---
##
✔ Final Answers:
1)
5
2)
12
3)
3
4)
6
5)
9
6)
10
7)
8
8)
1
9)
0
10)
11
11)
2
12)
6
---
Let me know if you’d like a printable version or further explanation on any part!
Parent Tip: Review the logic above to help your child master the concept of classifying polynomials worksheet.
