Podcast
Questions and Answers
What is a variable?
What is a variable?
A variable is a letter whose value is an unknown real number.
What is a term?
What is a term?
A term is a number, or product of a number and variable(s) raised to a power.
What is the coefficient of a term?
What is the coefficient of a term?
The coefficient of a term is the numerical factor.
If a term is a number only, it is called a constant term or simply a constant.
If a term is a number only, it is called a constant term or simply a constant.
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A letter that can be any one of various numbers is called a variable.
A letter that can be any one of various numbers is called a variable.
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What is a monomial?
What is a monomial?
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Which of the following are examples of monomials?
Which of the following are examples of monomials?
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A polynomial is usually written in descending order of powers.
A polynomial is usually written in descending order of powers.
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A polynomial with more than one variable is written in alphabetic order.
A polynomial with more than one variable is written in alphabetic order.
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What is the degree of a term?
What is the degree of a term?
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What is the leading term of a polynomial?
What is the leading term of a polynomial?
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What is the degree of a polynomial?
What is the degree of a polynomial?
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What are like terms?
What are like terms?
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Like terms can be added or subtracted.
Like terms can be added or subtracted.
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Xy is the same as yx.
Xy is the same as yx.
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What is the coefficient of the monomial 8x³?
What is the coefficient of the monomial 8x³?
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What is the coefficient of the monomial 3.7x⁰?
What is the coefficient of the monomial 3.7x⁰?
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To add polynomials horizontally, we use a ______ sign and add like terms.
To add polynomials horizontally, we use a ______ sign and add like terms.
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To subtract a polynomial, we change the sign of every term. This is the same as multiplying by ______.
To subtract a polynomial, we change the sign of every term. This is the same as multiplying by ______.
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To divide a polynomial by a constant, divide ______ of the polynomial by the constant.
To divide a polynomial by a constant, divide ______ of the polynomial by the constant.
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To divide a polynomial by a monomial, divide ______ of the polynomial by the monomial.
To divide a polynomial by a monomial, divide ______ of the polynomial by the monomial.
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What is the formula for the area of a rectangle?
What is the formula for the area of a rectangle?
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What is the formula for the volume of a rectangular prism?
What is the formula for the volume of a rectangular prism?
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Match the following geometric shapes to their respective formulas for calculating area:
Match the following geometric shapes to their respective formulas for calculating area:
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What is the definition of a factor?
What is the definition of a factor?
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What are the factors of 12?
What are the factors of 12?
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What is the definition of a multiple?
What is the definition of a multiple?
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What are the first five multiples of 3?
What are the first five multiples of 3?
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What is the formula for the perimeter of a square?
What is the formula for the perimeter of a square?
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What is the formula for the area of a square?
What is the formula for the area of a square?
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What is the formula for the circumference of a circle?
What is the formula for the circumference of a circle?
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Study Notes
Polynomials
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A variable is a letter representing an unknown real number (e.g., a, b, c, x, y, z).
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A term is a number or a product of a number and variable(s) raised to a power. (e.g., 5, 2x, 3x², 2xy).
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The coefficient of a term is its numerical factor (e.g., in 5x, the coefficient is 5; in 3x², the coefficient is 3) .
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A constant term is a number on its own (e.g., 5, -1.3).
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A monomial is an algebraic expression with one term (e.g., 3x², 7).
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A binomial is an algebraic expression with two terms (e.g., 2x - 1, x²-2xy).
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A trinomial is an algebraic expression with three terms (e.g., x² - 3x + 4).
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A polynomial is one term or a combination of sums or differences of monomials. (e.g., 3x, 2x - 1, 4x² + y + 2).
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The degree of a term is the sum of the exponents of its variables (e.g., in 5x², the degree is 2).
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The leading term of a polynomial is the term with the highest degree.
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The degree of a polynomial is the same as the degree of its leading term.
Like Terms
- Terms with the same variable raised to exactly the same powers are called like terms.
- Like terms can be added or subtracted.
- Unlike terms cannot be added or subtracted.
Simplifying Polynomials
- Combine like terms to simplify a polynomial.
Adding and Subtracting Polynomials
- Horizontally: Add or subtract like terms.
- Vertically: Arrange like terms in columns and add or subtract.
- Algebra tiles can be used as a visual aid to represent polynomials and their operations.
Multiplying Polynomials
- Multiply monomials by multiplying numerical factors and variables factors.
- Use the distributive property to multiply a polynomial by a monomial.
- Use algebra tiles to multiply polynomials visually.
Dividing Polynomials
- Dividing a polynomial by a constant: divide each term by the constant.
- Dividing a polynomial by a monomial: divide each term of the polynomial by the monomial.
- Use algebra tiles to visualize the division process.
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Description
Test your knowledge on polynomials, their terms, and classifications like monomials, binomials, and trinomials. This quiz will cover definitions, degrees, and the concept of like terms in algebra. Perfect for students looking to solidify their understanding of polynomial expressions.
