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Solving 7th-grade Math on pages 31 and 32, Volume 2, the Horizon of Creativity book provides step-by-step solutions for exercises 1 to 12 of the Univariate Polynomials lesson. For accurate solutions or helpful hints, refer to this useful resource.
Other 7th-grade math resources:
- Solving 7th-grade math, the Horizon of Creativity book
- Solving 7th-grade math on page 30, Volume 2, the Knowledge Connection book - Exercise: 25 Univariate Polynomials
- Solving 7th-grade math on pages 52 and 53, Volume 2, the Kite book - Exercise 2. Univariate Polynomials. Solutions of univariate polynomials
Solving exercises on pages 31 and 32 of the textbook, Volume 2, the Horizon of Creativity book
Univariate Polynomial
1. Solve Exercise 1 Page 31 Math Textbook Grade 7
Problem: Identify which of the following expressions is a univariate polynomial.
Solution:
A univariate polynomial is an algebraic expression containing only a number, a variable, or a product of numbers and that variable.
Answer:
Expressions a, c, and d are univariate polynomials.
Expression b is not a univariate polynomial.
2. Solve Exercise 2 Page 31 Math Textbook Grade 7
Problem: Identify which of the following expressions is a univariate polynomial.
Solution:
A univariate polynomial is the sum of monomials with the same variable.
A univariate monomial is also a univariate polynomial.
Answer:
Expressions A, B, M, N are univariate polynomials.
Expression Q is not a univariate polynomial.
3. Solving Exercise 3 Page 32 Math Textbook Grade 7
Problem: Determine the degrees of the following polynomials:
Solution:
The degree of a single-variable polynomial (different from a constant polynomial, which is already simplified) is the highest power of the variable in that polynomial.
Answer:
4. Solving Exercise 4 Page 32 Math Textbook Grade 7
Problem: Determine the coefficient and variable part of each polynomial:
Answer:
5. Solve Exercise 5 Page 32 Math Textbook Grade 7
Solution:
Simplify the polynomial by grouping terms with the same variable part and arranging polynomials in decreasing order of variable exponent.
Answer:
6. Solve Exercise 6 Page 32 Math Textbook Grade 7
Solution:
+ Simplify the polynomial by grouping terms with the same variable part and arrange polynomials in decreasing order of variable exponent.
+ The degree of a single-variable polynomial (different from a constant polynomial, already written in simplified form) is the highest power of the variable in that polynomial.
Answer:
+ Simplify the polynomial P(x):
+ The coefficient of the cubic term is -9.
The coefficient of the quadratic term is -1.
The coefficient of the linear term is -8.
7. Solve Exercise 7 Page 32 Math Textbook Grade 7
Problem: Calculate the values of the following polynomials:
Solution:
+ Substitute x = 2 into the expression P(x) and then calculate the value of the expression.
+ Substitute y = 3 into the expression Q(y) and then calculate the value of the expression.
Answer:
8. Solve Exercise 8 Page 32 Math Textbook Grade 7
Solution:
+ The degree of a single-variable polynomial (different from a constant polynomial, already written in simplified form) is the highest power of the variable in that polynomial.
+ Substitute t = 4 into the polynomial M(t) and then calculate the value of the polynomial.
Answer:
9. Solve Exercise 9 Page 32 Math Textbook Grade 7
Solution:
If the polynomial P(x) evaluates to 0 at x = a, then we say a (or x = a) is a root of that polynomial.
Answer:
10. Solve Exercise 10 Page 32 Math Textbook Grade 7
Solution:
If the polynomial P(x) evaluates to 0 at x = a, then we say a (or x = a) is a root of that polynomial.
Answer:
11. Solve Exercise 11 Page 32 Math Textbook Grade 7
12. Solve Exercise 12 Page 32 Math Textbook Grade 7
Problem: A kayak is moving with a velocity v = 16 + 2t (v in meters/second, t in seconds). Calculate the velocity of the kayak when t = 5.
Solution:
Substitute t = 5 into the expression v = 16 + 2t and then calculate the value of the expression.
Answer:
The speed of the kayak at t = 5 is:
v = 16 + 2(5) = 26.
Here is the guide to solving math problems for Grade 7, pages 31 and 32, Volume 2. Students can refer to the solutions for Grade 7 math problems on pages 35 and 36, Volume 2, and review Grade 7 math problems on page 28, Volume 2, to strengthen their knowledge.
- Grade 7 Math Solutions, pages 35 and 36, Volume 2, Chân Trời Sáng Tạo Book - Exercise 3: Adding and subtracting single-variable polynomials
- Grade 7 Math Solutions, page 40, Volume 2, Chân Trời Sáng Tạo Book - Exercise 4: Multiplying and dividing single-variable polynomials
