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Solving 7th-grade Math on page 30, Univariate Polynomial, Connecting Knowledge with Life Book, presents detailed and scientific solutions. It is not only a good study material for Univariate Polynomial lessons for students but also helps teachers prepare lessons easily, quickly, and accurately.
Other excellent 7th-grade Math study materials:
- Solving 7th-grade Math Connecting Knowledge with Life Book
- Solving 7th-grade Math on page 52, 53 Volume 2 Kite Book - Exercise 2. Univariate Polynomial. Solutions of Univariate Polynomials
- Solving 7th-grade Math on page 31, 32 Volume 2 Horizon of Creation Book - Exercise 2: Univariate Polynomial
Solving 7th-grade Math on page 30, Connecting Knowledge with Life Book
Univariate Polynomial
1. Solve Exercise 7.5 Page 30 Math Textbook Grade 7
Problem:
Solution:
To multiply two monomials, multiply the coefficients together and multiply the variable parts together.
To subtract two monomials, subtract the coefficients and keep the variable part unchanged.
The degree of a monomial with a non-zero coefficient is the sum of the exponents of all variables in that monomial.
Answer:
We have:
2. Solve Exercise 7.6 Page 30 Math Textbook Grade 7
Problem: Given two polynomials:
a) Condense and arrange the two polynomials according to the decreasing exponents of the variable.
b) Find the degree, leading coefficient, and constant term of each given polynomial.
Guidance:
In a condensed polynomial distinct from another polynomial:
+ The degree of the term with the highest degree is called the degree of that polynomial.
+ The coefficient of the term with the highest degree is called the leading coefficient of that polynomial.
+ The coefficient of the term with degree 0 is called the constant term of that polynomial.
Answer:
a) We have:
b) + Polynomial A(x) has degree 4.
The leading coefficient of the polynomial A(x) is -7.
The constant term of the polynomial A(x) is 9.
+ Polynomial B(x) has degree 4.
The leading coefficient of the polynomial A(x) is 8.
The constant term of polynomial A(x) is -7.
3. Solve Exercise 7.7 Page 30 Math Textbook Grade 7
Problem: Given two polynomials:
a) Condense and arrange the polynomial in decreasing order of variable exponents.
b) Use the result from part a to calculate P(1), P(0), Q(-1), and Q(0).
Guidance:
a) Combine and simplify like terms to condense the polynomial. Arrange the polynomial in decreasing order of variable exponents.
b) Substitute x = 1; x = 0 into polynomial P(x) and then calculate the value of the expression.
Substitute x = -1; x = 0 into polynomial Q(x) and then calculate the value of the expression.
Answer:
a) We have:
4. Solve Exercise 7.8 Page 30 Math Textbook Grade 7
b) Using the result from part a to calculate P(1), P(0), Q(-1), and Q(0).
Answer:
a) We have:
Volume of the tank = Volume of water pumped by the first pump in x hours + Volume of water pumped by the second pump in x hours + Volume of water pumped by the second pump in 0.5 hours + 1.5.
Answer:
The polynomial (in terms of x) representing the tank volume is:
A(x) = 1.5 + 22x + 16x + 0.5*16 = 38x + 9.5
The polynomial A(x) = 38x + 9.5 has the leading coefficient of 38 and the constant term: 9.5.
5. Solve Exercise 7.9 Page 30 Math Textbook Grade 7
Problem: Write a polynomial F(x) that simultaneously satisfies the following conditions:
The degree of F(x) is 3.
The coefficient of x2 equals the coefficient of x and equals 2.
The leading coefficient of F(x) is -6, and the constant term is 3.
Guide to Solve:
In a simplified polynomial distinct from another polynomial:
+ The degree of the term with the highest degree is called the degree of that polynomial.
+ The coefficient of the term with the highest degree is called the leading coefficient of that polynomial.
+ The coefficient of the constant term (degree 0) is called the constant coefficient of that polynomial.
Answer:
The polynomial F(x) satisfying the given conditions is:
6. Solve Exercise 7.10 Page 30 Mathematics Grade 7
Problem: Check if:
Solution:
If at x = a, the polynomial F(x) has a value of 0, i.e., F(a) = 0, then we call a (or x = a) a root of the polynomial F(x).
Answer:
b) We have:
7. Solve Exercise 7.11 Page 30 Mathematics Grade 7
Problem: Mother gave Quynh 100 thousand dong. Quynh bought a learning kit for 37 thousand dong and a reference book for the subject of Mathematics with the price of x (thousand dong).
a) Find the polynomial (variable x) representing the remaining amount of money Quynh has (unit: thousand dong). Find the degree of that polynomial.
b) After buying the book, Quynh spent exactly the amount of money her mother gave. Ask, how much is the price of the book?
Guidance:
a) + Write the polynomial (variable x) representing the remaining amount of money Quynh has.
+ In a polynomial, other than the zero polynomial, once simplified, the degree of the polynomial is the degree of the term with the highest degree.
b) Find x so that the value of the polynomial equals 0.
Answer:
a) The polynomial (variable x) representing the remaining amount of money Quynh has (unit: thousand dong) is:
Q(x) = 100 - (37 + x) = 63 - x.
The polynomial Q(x) has a degree of 1.
b) After buying the book, Quynh spends exactly the amount her mother gave her, so: Q(x) = 0.
It follows that 63 - x = 0.
=> x = 63.
So, the price of the book is 63 thousand dong.
Here is the guide for solving math class 7 page 30 volume 2. Students can also refer to solving math class 7 page 33 volume 2 and review solving math class 7 page 24 volume 2 to ensure understanding.
- Solving math class 7 page 33 volume 2, Connecting Knowledge - Exercise: 26 Polynomial Addition and Subtraction
- Solving math class 7 page 24 volume 2, Connecting Knowledge - Exercise 24: Algebraic Expressions
