Let's solve each problem step by step. The
degree of a polynomial is the
highest degree of its terms, where the degree of a term is the
sum of the exponents of the variables in that term.
---
1) $ x^2 + 8 - 5x^2y + xy^2 $
- Term $ x^2 $: degree = 2
- Term $ 8 $: constant → degree = 0
- Term $ -5x^2y $: $ x^2 \cdot y $ → degree = 2 + 1 = 3
- Term $ xy^2 $: $ x \cdot y^2 $ → degree = 1 + 2 = 3
→ Highest degree =
3
✔ Answer: 3
---
2) $ s^5 - 2q^4r^4s $
- Term $ s^5 $: degree = 5
- Term $ -2q^4r^4s $: $ q^4 \cdot r^4 \cdot s $ → degree = 4 + 4 + 1 = 9
→ Highest degree =
9
✔ Answer: 9
---
3) $ m - 7 - m^3 - m^2 $
- Term $ m $: degree = 1
- Term $ -7 $: degree = 0
- Term $ -m^3 $: degree = 3
- Term $ -m^2 $: degree = 2
→ Highest degree =
3
✔ Answer: 3
---
4) $ -y^6 + z^2 + 6 - 4z^2 + 5y^3 $
- Term $ -y^6 $: degree = 6
- Term $ z^2 $: degree = 2
- Term $ 6 $: degree = 0
- Term $ -4z^2 $: degree = 2
- Term $ 5y^3 $: degree = 3
→ Highest degree =
6
✔ Answer: 6
---
5) $ 7a^2 + b^6 + 5 + c + a^4b^2c^3 $
- Term $ 7a^2 $: degree = 2
- Term $ b^6 $: degree = 6
- Term $ 5 $: degree = 0
- Term $ c $: degree = 1
- Term $ a^4b^2c^3 $: $ 4+2+3 = 9 $
→ Highest degree =
9
✔ Answer: 9
---
6) $ u^6 - 8v^3 - 9u^4v^3 $
- Term $ u^6 $: degree = 6
- Term $ -8v^3 $: degree = 3
- Term $ -9u^4v^3 $: $ 4+3 = 7 $
→ Highest degree =
7
✔ Answer: 7
---
7) $ -m^2 - 2n + m^3n^3 - 4 - 5n^3 $
- Term $ -m^2 $: degree = 2
- Term $ -2n $: degree = 1
- Term $ m^3n^3 $: $ 3+3 = 6 $
- Term $ -4 $: degree = 0
- Term $ -5n^3 $: degree = 3
→ Highest degree =
6
✔ Answer: 6
---
8) $ -3 + 4a $
- Term $ -3 $: degree = 0
- Term $ 4a $: degree = 1
→ Highest degree =
1
✔ Answer: 1
---
9) $ -10 $
- Constant term only → degree =
0
✔ Answer: 0
---
10) $ 9x^3y + y^2\ell^6 + 3\ell^3 - 7x\ell^2 - s^3 - 2\ell^2 $
Note: Variables are $ x, y, \ell, s $. Let’s compute each term:
- $ 9x^3y $: $ 3+1 = 4 $
- $ y^2\ell^6 $: $ 2+6 = 8 $
- $ 3\ell^3 $: degree = 3
- $ -7x\ell^2 $: $ 1+2 = 3 $
- $ -s^3 $: degree = 3
- $ -2\ell^2 $: degree = 2
→ Highest degree =
8
✔ Answer: 8
---
11) $ p^3 + 6q $
- Term $ p^3 $: degree = 3
- Term $ 6q $: degree = 1
→ Highest degree =
3
✔ Answer: 3
---
12) $ u^2v^2w^2 + 2uv - 7v - u^2 $
- Term $ u^2v^2w^2 $: $ 2+2+2 = 6 $
- Term $ 2uv $: $ 1+1 = 2 $
- Term $ -7v $: degree = 1
- Term $ -u^2 $: degree = 2
→ Highest degree =
6
✔ Answer: 6
---
✔ Final Answers:
1)
3
2)
9
3)
3
4)
6
5)
9
6)
7
7)
6
8)
1
9)
0
10)
8
11)
3
12)
6
Let me know if you'd like this formatted as a table or printable sheet!
Parent Tip: Review the logic above to help your child master the concept of polynomial functions worksheet.
