To solve this worksheet, we need to
identify the degree of each polynomial.
---
🔍 What is the degree of a polynomial?
The
degree of a polynomial is the
highest exponent of any term in the polynomial. For
multivariable polynomials, you add the exponents of all variables in each term, and then take the
highest sum among all terms.
---
Let’s go through each problem one by one:
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1) `s + k - n - r - p + z`
- All variables are to the power of 1 (e.g., s = s¹, k = k¹, etc.)
- No exponents shown → assumed to be 1.
- So, each term has degree 1.
✔ Degree = 1
---
2) `-3qx - 8h`
- Term 1: `-3qx` → q¹x¹ → total degree = 1 + 1 =
2
- Term 2: `-8h` → h¹ → degree =
1
- Highest degree = 2
✔ Degree = 2
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3) `-9hd⁶h`
Wait — let’s simplify this first:
- `-9hd⁶h` = `-9h²d⁶` (since h × h = h²)
- Exponents: h² → 2, d⁶ → 6 → total degree = 2 + 6 =
8
✔ Degree = 8
---
4) `-z + d - n + c`
- All variables have exponent 1.
✔ Degree = 1
---
5) `-cx - 7r`
- Term 1: `-cx` → c¹x¹ → degree = 1 + 1 =
2
- Term 2: `-7r` → r¹ → degree =
1
✔ Degree = 2
---
6) `-z`
- Single variable, exponent 1.
✔ Degree = 1
---
7) `-4r⁴c⁵ - 7n³`
- Term 1: `-4r⁴c⁵` → r⁴c⁵ → 4 + 5 =
9
- Term 2: `-7n³` → n³ → degree =
3
✔ Degree = 9
---
8) `-7ks³ - 6b⁴`
- Term 1: `-7ks³` → k¹s³ → 1 + 3 =
4
- Term 2: `-6b⁴` → b⁴ → degree =
4
✔ Degree = 4
---
9) `k - c - q`
- All variables to power 1.
✔ Degree = 1
---
10) `-8q⁶h³r⁴ + 9s⁷ + 4n⁷d⁶ + 5d⁴b⁶`
Let’s compute degree of each term:
- Term 1: `-8q⁶h³r⁴` → 6 + 3 + 4 =
13
- Term 2: `9s⁷` → s⁷ →
7
- Term 3: `4n⁷d⁶` → 7 + 6 =
13
- Term 4: `5d⁴b⁶` → 4 + 6 =
10
Highest degree among these is
13
✔ Degree = 13
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##
✔ Final Answers:
1)
1
2)
2
3)
8
4)
1
5)
2
6)
1
7)
9
8)
4
9)
1
10)
13
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📌
Tip: Always check if variables are multiplied together — their exponents add up for the term’s degree. The overall degree is the highest among all terms.
Let me know if you want a printable answer key or explanation sheet!
Parent Tip: Review the logic above to help your child master the concept of monomial binomial trinomial polynomial worksheet.
