Let’s go through each problem one by one.
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Problem 1:
*The number part of a term is called the __________.*
In algebra, every term has two parts: a number and a variable (like x or y). The number that multiplies the variable is called the
coefficient. For example, in “5x”, 5 is the coefficient.
✔ Answer:
coefficient
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Problem 2:
*If a term in a polynomial only has a number part, it’s called a ________ term.*
When there’s no variable — just a plain number like 7 or -3 — we call that a
constant term because it doesn’t change.
✔ Answer:
constant
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Problem 3:
*How many terms does this polynomial have?*
5x³ – x² + 5x – 8
A “term” is each separate piece added or subtracted. Let’s count them:
- 5x³ → 1st term
- –x² → 2nd term
- +5x → 3rd term
- –8 → 4th term
That’s 4 terms total.
✔ Answer:
4
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Problem 4:
*Write the degree of each of these terms:*
Recall: The
degree of a term is the sum of the exponents on the variables.
-
3x² → exponent is 2 → degree =
2
-
10x → same as 10x¹ → exponent is 1 → degree =
1
-
6x³ → exponent is 3 → degree =
3
-
x²y² → add exponents: 2 + 2 = 4 → degree =
4
✔ Answers:
3x² →
2
10x →
1
6x³ →
3
x²y² →
4
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Problem 5:
*What is the coefficient of the 3rd degree term in this polynomial?*
3x² + x – 2x³ – 10
First, let’s rewrite the polynomial in order from highest to lowest degree (standard form) to make it easier:
–2x³ + 3x² + x – 10
Now, the 3rd degree term is
–2x³
Its coefficient is
–2
✔ Answer:
–2
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Problem 6:
*What is the coefficient of the 2nd degree term in this polynomial?*
x² + 2x – 5
The 2nd degree term is
x², which is the same as
1x²
So the coefficient is
1
✔ Answer:
1
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Problem 7:
*What is the degree of this polynomial?*
4x⁵ – 3x² + x
The degree of a polynomial is the highest degree among its terms.
- 4x⁵ → degree 5
- –3x² → degree 2
- x → degree 1
Highest is 5.
✔ Answer:
5
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Problem 8:
*What is the degree of this polynomial?*
4xy – 3y + 8
Look at each term:
- 4xy → x¹y¹ → 1+1 =
2
- –3y → y¹ →
1
- 8 → constant →
0
Highest degree is 2.
✔ Answer:
2
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Problem 9:
*Re-arrange this polynomial so its terms are in order from highest to lowest.*
5x + 2x³ – 15 – 7x²
List all terms with their degrees:
- 2x³ → degree 3
- –7x² → degree 2
- 5x → degree 1
- –15 → degree 0
Order from highest to lowest degree:
2x³ – 7x² + 5x – 15
✔ Answer:
2x³ – 7x² + 5x – 15
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Problem 10:
*Re-arrange this polynomial so its terms are in order from highest to lowest.*
7 + 2xy – 4x³y + 5x
Find the degree of each term:
- 7 → constant → degree 0
- 2xy → x¹y¹ → 1+1 =
2
- –4x³y → x³y¹ → 3+1 =
4
- 5x → x¹ →
1
Order from highest to lowest degree:
–4x³y + 2xy + 5x + 7
✔ Answer:
–4x³y + 2xy + 5x + 7
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Final Answer:
1. coefficient
2. constant
3. 4
4. 2, 1, 3, 4
5. –2
6. 1
7. 5
8. 2
9. 2x³ – 7x² + 5x – 15
10. –4x³y + 2xy + 5x + 7
Parent Tip: Review the logic above to help your child master the concept of simplifying polynomials worksheet.
