9 Questions
What is the degree of the polynomial 2x^4 - 3x^3 + 5x^2 - x + 1?
4
What is the result of adding the polynomials (2x^2 + 3x - 1) and (x^2 - 2x - 3)?
3x^2 + x - 4
Which of the following is NOT a term in the polynomial 3x^2 + 2x - 4?
x
What is the coefficient of x^2 in the polynomial 3x^2 + 2x - 4?
3
Which of the following is an example of a constant?
2
What is the result of subtracting the polynomial x^2 - 2x - 3 from the polynomial 2x^2 + 3x - 1?
x^2 + 5x - 2
Which of the following polynomials has a degree of 3?
x^3 + 2x^2 - x + 1
What is the result of adding the polynomial 2x^2 + 3x - 1 to itself?
4x^2 + 6x - 2
Which of the following is an example of a variable?
x
Study Notes
Algebra
- Definition: Algebra is a branch of mathematics that deals with the study of variables and their relationships, often expressed through the use of symbols, equations, and functions.
- Equations: An equation is a statement that says two expressions are equal, often denoted by the "=" symbol. Examples: 2x + 3 = 5, x^2 - 4 = 0.
- Variables: A variable is a letter or symbol that represents a value that can change. Examples: x, y, z.
- Constants: A constant is a value that does not change. Examples: 2, 5, -3.
Polynomials
- Definition: A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
- Examples: 3x^2 + 2x - 4, x^3 - 2x^2 - x + 1, 2x - 5.
- Degree: The degree of a polynomial is the highest power of the variable. Examples: 3x^2 + 2x - 4 has a degree of 2, x^3 - 2x^2 - x + 1 has a degree of 3.
- Terms: A term is a part of a polynomial separated by addition or subtraction. Examples: 3x^2, 2x, -4 are terms in the polynomial 3x^2 + 2x - 4.
- Coefficients: A coefficient is a number multiplied by a variable in a polynomial. Examples: 3 is the coefficient of x^2, 2 is the coefficient of x in the polynomial 3x^2 + 2x - 4.
- Like Terms: Like terms are terms with the same variable and exponent. Examples: 2x and 3x are like terms, x^2 and 2x^2 are like terms.
- Adding and Subtracting Polynomials: To add or subtract polynomials, combine like terms. Example: (2x^2 + 3x - 1) + (x^2 - 2x - 3) = 3x^2 + x - 4.
Algebra
- Algebra is a branch of mathematics that deals with the study of variables and their relationships.
- Variables are letters or symbols that represent values that can change.
- Constants are values that do not change.
Equations
- An equation is a statement that says two expressions are equal.
- Equations are often denoted by the "=" symbol.
- Examples of equations include 2x + 3 = 5 and x^2 - 4 = 0.
Polynomials
- A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
- Examples of polynomials include 3x^2 + 2x - 4, x^3 - 2x^2 - x + 1, and 2x - 5.
- The degree of a polynomial is the highest power of the variable.
- Examples of degrees include 2 for 3x^2 + 2x - 4 and 3 for x^3 - 2x^2 - x + 1.
Terms and Coefficients
- A term is a part of a polynomial separated by addition or subtraction.
- Examples of terms include 3x^2, 2x, and -4 in the polynomial 3x^2 + 2x - 4.
- A coefficient is a number multiplied by a variable in a polynomial.
- Examples of coefficients include 3 for x^2 and 2 for x in the polynomial 3x^2 + 2x - 4.
Like Terms and Operations
- Like terms are terms with the same variable and exponent.
- Examples of like terms include 2x and 3x, as well as x^2 and 2x^2.
- To add or subtract polynomials, combine like terms.
- Example: (2x^2 + 3x - 1) + (x^2 - 2x - 3) = 3x^2 + x - 4.
Learn the fundamentals of algebra, including equations, variables, and constants. Understand how to work with symbols, equations, and functions.
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